Rip 


IN  MEMORIAM 
FLOR1AN  CAJOR1 


PRIMARY   ARITHMETIC 


BY 


BRUCE   M.    WATSON 

SUPERINTENDENT  OF  SCHOOLS, 
SPOKANE,  WASHINGTON 


CHARLES   E.    WHITE 

PRINCIPAL  OF  FRANKLIN   SCHOOL,   SYRACUSE,  M.Y. 


D.    C.    HEATH   &   CO.,   PUBLISHERS 

BOSTON        NEW   YORK         CHICAGO 


Copyright,  1906, 
By  D.  C.  HEATH  &  CO. 


1f2 


INTRODUCTION 

In  the  preparation  of  this  series  of  arithmetics  the  aims  have 
been: 

First,  —  To  secure  a  high  degree  of  facility  in  the  funda- 
mental operations  and  in  those  other  processes  which,  in  the 
actual  business  of  life,  are  reduced  to  purely  mechanical  forms 
of  computation. 

Second,  —  To  cultivate  in  pupils  the  habit  of  forming  vivid 
mental  pictures  of  the  business  transactions  introduced  in  the 
exercises,  and  of  the  commercial  and  industrial  relations  of  the 
numbers  involved  in  the  problems. 

Third,  —  To  make,  at  proper  times,  a  clear  and  rational  de- 
velopment of  so  much  of  the  theory  of  numbers  as  is  necessary 
for  intelligent  arithmetical  work. 

Fourth,  —  To  grade  the  work  up,  from  the  simple  and  easy 
to  the  more  complex  and  difficult,  by  steps  so  gradual  and  in 
an  order  so  logical,  that  the  pupil  will  steadily  grow  in  mathe- 
matical power  and  take  pleasure  in  his  own  progress. 

In  pursuance  of  the  aims  herein  outlined,  care  has  been 
taken  to  dwell  upon  each  new  process  until  the  child  has  ac- 
quired a  considerable  degree  of  skill  in  it.  Then  it  has  not 
been  permitted  to  drop  out  of  sight  and  memory,  but  has  been 
kept  fresh  by  continuous  and  systematic  review. 

Ill 


JV  INTRODUCTION 

Useless  and  meaningless  distinctions  and  statements  of  matter 
have  been  avoided. 

The  problems  of  play,  of  trade,  and  of  industry  deal  with 
things  and  transactions  that  are  within  the  experience  or  knowl- 
edge of  the  child  and  appeal  to  his  interest. 

The  numbers  used  in  problems  are  not  so  large  as  to  cause 
fatigue,  discouragement,  or  waste  of  time. 

In  the  development  work,  pupils  are  directed  in  a  line  of 
observation  or  experiment  and  enabled  to  obtain  their  facts 
from  the  numbers  and  objects  studied,  rather  than  from  a 
printed  statement. 

The  present  volume  is  intended  to  cover  the  work  usually 
accomplished  during  the  first  four  years  of  school. 

The  text-book  may  be  introduced  either  in  the  middle  of  the 
second  year,  or  at  the  beginning  of  the  third.  When  the 
former  plan  is  chosen,  the  first  thirty-one  pages,  consisting 
of  oral  work  involving  all  combinations  of  numbers  to  twenty- 
four,  will  be  found  to  contain  sufficient  book  work  for  the  re- 
mainder of  the  second  year.  When  the  latter  plan  is  followed, 
the  pages  covering  work  that  has  been  accomplished  orally  in 
the  second  year  will  serve  as  review  and  preparation  for  the 
lessons  that  follow. 

The  further  distribution  of  the  course  through  the  third  and 
fourth  years  must  be  determined  by  local  conditions,  experi- 
ence, and  age  of  pupils. 


0 


CONTENTS 

PAGE 

PAGE 

Counting     .... 

1 

Quart,  Peck,  and  Bushel    . 

72 

Reading  and  Writing  Numbers 

3 

Review        .         .         .         .         . 

73 

Combinations  to  12    . 

4 

Division 

75 

Combinations  of  Two 

10 

Review 

79 

Counting  by  2's  . 

13 

Multiplication  and  Division 

80 

Problems     .... 

14 

Review 

81 

Yard  and  Foot   . 

15 

Telling  Time      .        .        .         . 

83 

Three.        . 

16  (^Reading  and  Writing  Numbers 

84 

One  Third  .         .         .         . 

17  " 

Oral  Practice  in  Numbers  . 

85 

Gallon        .... 

18 

Written  Practice  in  Numbers    . 

87 

Two,  Three,  and  Four 

19 

Review 

88 

One  Fourth         .         .         . 

20 

Multiplication  by  10,  100,  1000 . 

89 

Five 

21 

Quick  Test          .         .         .         . 

91 

Foot  and  Inch    . 

22 

Days  in  the  Different  Months    . 

92 

Six,  Seven,  Eight 

24 

Finding  Any  Part  of  a  Num- 

Combinations to  24    . 

27 

ber  

93 

Drill  Tables 

31 

Miscellaneous  Problems     . 

94 

Reading  and  Writing  Numbers: 

32 

Quick  Test         .        .        .        . 

95 

Addition     .... 

33 

Review 

97 

Problems  in  Addition 

43 

Miscellaneous  Examples     . 

98 

Subtraction 

46 

Multiplication  and  Division  by 

Oral  and  Written  Addition  anc 

I 

Multiples  of  10 

100 

Subtraction 

47 

Review 

101 

Problems  in  Temperature  . 

54 

Pound  and  Ounce 

103 

Review         .... 

56 

Review 

104 

Multiplication     . 

.     61 

Division 

105 

Review        .... 

.     63 

Quick  Test          . 

107 

Roman  Numerals 

.     64 

Review 

108 

Division      .... 

.     65 

Multiplication  and  Division 

109 

Review        .... 

.     66 

Making  Questions 

110 

Multiplication     . 

.     69 

Review 

111 

VI 


CONTENTS 


PAGE 

Rectangles 112 

Multiplication  and  Division  .  114 
Making  Change .  .  .  .  116 
Roman  Numerals  .  .  .  116 
Miscellaneous  Problems     .         .117 

-  Halves,  Fourths,  and  Eighths  .  122 
Miscellaneous  Problems     .         .  123 

^Reading  and  Writing  Numbers  124 

Review 125 

Multiplication  and  Division       .  126 

Perimeter 127 

Multiplication  and  Division       .  128 

Area 131 

Division 132 

Review 133 

Odd  and  Even  Numbers'  .         .  141 

Factors 142 

Quick  Test 143 

Factors 144 

Multiples 145 

Fractions 146 

Whole  and  Mixed  Numbers       .  149 


PAGE 

155 
157 
161- 
163 
165 
166 
175 


Review  .... 
Adding  Fifths  and  Halves 
Adding  Fourths  and  Fifths 
Adding  Fourths  and  Thirds 
Adding  Halves  and  Sevenths 
Review  and  Practice  . 
United  States  Money 
Review  and  Practice  .  .  .176 
Liquid  Measure  .  .  .  .179 
Dry  Measure       .        .        .        .181 

Time 183 

Avoirdupois  Weight  .  .  .187 
Linear  Measure  .  .  .  .188 
Review  and  Practice  .  .  .  190 
Surface  Measure  .         .         .194 

Prime  and  Composite  Numbers  199 
Prime  Factors  .  .  .  .200 
Factors  and  Multiples  .  .  201 
Cancellation        .        .         .        .202 

Review 205 

Multiplication  Table  .  .  .205 
Tables  of  Denominate  Numbers  210 


PRIMARY 
ARITHMETIC 


PRIMARY   ARITHMETIC 


COUNTING 

i.  Count  to  twenty. 

2.  How  many  boys  are  there  in  your  class  ? 

3.  Count  the  children  in  the  class. 

4.  How  many  desks  are  there  in  your  row  ? 

5.  Find  twelve  pieces  of  chalk. 

6.  Find  eleven  sticks. 

7.  Lay  four  sticks  so  as  to  make  a  square. 

8.  Lay  four  sticks  so  as  to  make  a  chair. 

9.  Lay  eight  sticks  so  as  to  make  two  squares. 

10.  How  many  squares  can  you  make  with  twelve 
sticks  ? 

Note.  —  These  exercises  are  suggestive  of  many  that  may  be  given. 

ii.  Write  the  figures  for  one,  two,  three,  four,  five,  six, 
seven,  eight,  nine. 

12.  Tell  as  quickly  as  "you  can  the  number  of  spots  on 
each  of  these  dominoes : 


•  •  ••  •  •         •     •    •    • 

•  •  •••  ••••• 


WRITING   NUMBERS 


l.   Take  ten  sticks.     Tie  them  in  a  bundle,  thus,  g& 


11 


2.  Count  out  ten  such  bundles,  and  call  each 
bundle  "a  ten." 

3.  Put  one  bundle  on  the  table. 

4.  Put  one  stick  beside  it,  thus,  1  1 
How  many  sticks  are  there  ?                    Bftjj 

5.  Put  another  stick  with  it,  thus, 

How  many  sticks  are  there  ?  12         Sill 

6.  Take  another  ten  and  put  three  with  it,  thus,  j 
How  many  are  there  ?  13 

Go  on  in  this  way  to  nineteen. 

7.  What  does  the  figure  1  stand  for  in  the  number  12  ? 

8.  What  does  the  figure  1  stand  for  ?   in  13,  14,  15, 
16,  17,  18,  19  ? 

9.  How  many  tens  are  there  in  11  ?    How  many  over  ? 
In  14,  15,  16,  17,  18,  19?  g 

io.    In  writing  ten  we  use  the  figure  1  for  the  ten    m 
bundle  and  O  to  show  that  there  is  none  over,  thus,       ^q 

li.    Take  two  tens.     How  many  sticks  in  all  ? 
12.    To  write  twenty,  we  use  2  to  stand  for  2  tens 
and  O  to  show  that  there  is  none  over,  thus,  ^q 


13.  Take  two  tens  and  one,  thus, 
How  many  ?     Write  it,  thus,  2     1 

14.  Lay  counters  for  22,  23,  25,  27,  29. 

15.  Lay  counters  for  thirty,  thirty-one,  forty-three. 


READING  AND   WRITING  NUMBERS 


3 


1.  Write  fifteen  ;  twenty ;  eighteen ;  fourteen. 

2.  Write  twenty-five  ;  thirty-seven ;  forty ;  ninety-six. 

3.  Write  eighty-two  ;  seventy ;  forty-nine  ;  sixty-one. 

4.  Write  the  number  of  desks  in  your  room. 

5.  Write  the  number  of  stars  on  our  flag. 

6.  Write  your  own  age. 

7.  Count  fifty,  forward  and  backward. 

8.  Write  in  words  16,  19,  20,  43,  69,  38,  42,  71. 

9.  Write  the  number  of  books  on  the  teachers  desk. 
io.    Write  the  number  of  panes  of  glass  in  your  school- 
room. 

li.   Read  25,  21,  38,  45,  36,  28,  72,  64. 
Write  them  in  a  column  so  that  the  tens  will  be  in  a 
vertical  line. 

12.  Count  forward  and  backward  from  50  to  100. 

13.  Write  in  figures  all  the  numbers  to  one  hundred 
that  have  0's  in  them. 

14.  Write  in  figures  and  in  words  the  number  of  desks 
in  your  row. 

15.  Write  in  figures  and  in  words  the  number  of  letters 
in  your  name.  * 

is.   Read  15,  37,  58,  34,  96,  82,  67,  77,  17,  83,  39,  51. 

17.  Write  in  figures,  ninety-one,  twenty-seven,  sixty-eight, 
ninety-three,  thirty-five,  fifty-three. 

18.  Write  the  number  of  squares 
in  this  drawing. 

19.  Write  the  number  of  dots. 


•  •        •        • 

•  •        •        • 

•  •        •        • 

•  •        •        • 


COMBINATIONS  TO   12 


1.  There  are  how  many  drums  in  this  picture  ? 

2.  One  is  a  bass  drum.     How  many  other  drums  are 
there  ?     How  many  fifes  are  there  ? 

3.  How  many  more  drums  than  fifes  are  there  ? 

4.  Four  fifers,  one  color  bearer,  and  one    leader  are 
how  many  boys  ? 

5.  Four  fifers  and  six  drummers  are  how  many  boys  ? 

6.  If  the  boys  march  around  two  squares,  how  many 
blocks  will  they  march  ?     Draw  the  squares. 

7.  If  they  march  three  blocks  away,  and  then  back  to 
the  starting  place,  how  many  blocks  do  they  march  ? 

8.  If  they  march  2  miles  on  Monday  and  3  miles  on 
Tuesday,  how  many  miles  do  they  inarch  in  both  days  ? 

9.  When  they  march  3  blocks  with  music  and  4  blocks 
without,  how  many  blocks  do  they  march  ? 

io.  When  they  march  around  the  square  twice,  how 
many  blocks  do  they  go  ?     Make  a  picture  of  the  square. 

11.  If  they  have  marched  9  blocks  away  from  home 
and  5  blocks  toward  home,  how  far  from  home  are  they? 


COMBINATIONS   TO    12 

Keep  pint  and  quart  measures  before  pupils. 

What  is  the  first  measure  ? 

For  what  do  we  use  it  ? 

What  is  the  second  measure  ? 

For  what  do  we  use  it?     Which 
is  the  larger  ? 

Fill  the  pint  measure  with  water.  Pour  it  into  the 
quart  measure.  Do  it  again.  How  much  more  will  the 
quart  measure  hold  ?  How  many  pints  does  the  quart 
measure  hold  ? 

1.  How  many  pints  make  a  quart? 

2.  The  quart  measure  will  fill  the  pint  measure  how 
many  times  ? 

3.  Two  quarts  are  how  many  pints  ?  Measure  and 
prove  it.     Three  quarts  ?     Four,  five,  six  quarts  ? 

4.  How  many  quarts  are  there  in  4  pt.  ?  Six,  eight, 
ten,  twelve  pints?     (pt.  stands  for  pint  or  pints) 

5.  Mary  bought  3  quarts  of  milk.  How  many  pints 
did  she  buy  ? 

6.  Alice  filled  a  pint  measure  four  times  from  a  pitcher 
of  water.  How  many  times  would  the  pitcher  of  water 
fill  a  quart  measure  ?     Why? 

7.  How  many  pint  bottles  can  be  filled  from  five 
quarts  of  cream  ? 

8.  How  many  quart  cans  will  12  pints  of  sirup  fill  ? 

9.  How  many  pints  of  milk  will  3  pint  bottles  and 
one  quart  bottle  hold  ? 


6  COMBINATIONS  TO   12 

1.  I  spent  2  cents  for  a  yeast  cake,  and  4  cents  for 
candy.     How  much,  did  both  cost? 

2.  Mary  had  3  red  roses  and  two  yellow  ones.     How 
many  had  she  in  all  ? 

3o   Two  birds  have  how  many  wings  ? 

4.  Four  boys  have  how  many  thumbs  ? 

5.  Three  horses  have  how  many  ears  ? 

6.  If  we  work  six  days  in  a  week,  how  many  days  do 
we  rest  ? 

7.  Two  dogs  have  how  many  feet  ? 

8.  A  dime  is  made  of  silver.     It  is  the  same  as  ten 
cents. 

A  dime  less  two  cents  is  how  many  cents  ? 

9.  How  many  oranges  are  there  in  a  dozen  ? 

10.  Find  the  cost  of  3  pranges  at  2  cents  apiece. 

11.  Add: 

4632272125 
1122423421 
3112213332 

12.  Subtract : 

6475488458 
22    3    2457332 

13.  Count  by  2's  from  1  to  11. 

14.  Count  by  2's  from  2  to  10. 
is.  Count  by  2's  from  10  to  2. 
16.  Count  by  2's  from  11  to  1. 


COMBINATIONS   TO   12 

1.  What  two  numbers  added  make  3  ? 

2.  Add.  two  numbers  to  make  5. 

3.  Add  two  numbers  to  make  4. 

4.  Add  two  numbers  to  make  6. 

5.  What  two  numbers  added  make  7  ? 

6.  What  three  numbers  added  make  7  ? 

7.  What  three  numbers  added  make  10  ? 

8.  What  three  numbers  added  make  8  ? 

9.  What  three  numbers  added  make  9  ? 

10.  Count  to  12  by  fours. 

11.  Count  to  12  by  threes. 


12. 

6  +  ?=8 

9-?=3 

7  +  2  =  ? 

5  +  ?=9 

13. 

7  +  ?=9 

9-?=7 

6  +  3  =  ? 

3  +  ?  =  9 

14. 

2  +  ?=5 

6-?-2 

7-2  =  ? 

5  +  ?  =  7 

15. 

5  +  ?=9 

10-t-4 

?-4  =  6 

?-6  =  4 

16. 

3  +  ?=6 

7-?=2 

?+3  =  6 

7-5  =  ? 

17.   Name  the  days  of  the  week. 

is.   Which  is  the  first  day  ?    The  fourth?    The  seventh? 

19.  How  many  working  days  in  two  weeks  ? 

20.  How  many  days  are  2  days  less  than  a  week  ? 
2i.   A  week  and  3  days  are  how  many  days  ? 

22.  There  were  7  apples  in  a  basket.     Frank  took  1  in 
each  hand.     How  many  were  left  ? 

23.  Eight   boys   went   to   the   store   for   milk.      Each 
bought  a  pint.     How  many  quarts  did  they  buy  ? 


8  COMBINATIONS   TO   12 

Many  years  ago,  the  Romans  wrote  numbers  by  means 
of  letters.  We  use  letters  to  make  the  numbers  on  the 
face  of  the  clock,  to  number  the  chapters  in  a  book,  and 
for  a  few  other  purposes. 

The  Roman  way  of  writing  the  first  five  numbers  is 
this: 

I  stands  for  one.  Ill  stands  for  three. 

II  stands  for"  two.  IV  stands  for  four. 

V  stands  for  five. 

1.  Using  letters,  write  the  number  of  eyes  you  have ; 
the  number  of  thumbs  on  one  hand  ;  the  number  of  fingers 
on  one  hand ;  the  number  of  quarts  in  six  pints  ;  the  num- 
ber of  school  days  in  a  week. 

2.  When  you  attend  school  only  3  days  in  a  week, 
how  many  days  are  you  absent  ? 

3.  When  the  sun  shines  only  three  days  in  a  week, 
how  many  days  are  cloudy  ? 

4.  Frank  earned  10  cents  and  gave  his  sister  2  cents. 
How  much  money  had  he  left  ? 

5.  Lucy  has  3  cents.  How  many  more  cents  must  she 
have  to  buy  a  ten-cent  jumping  rope  ? 

6.  If  Will  earned  2  cents  on  Monday,  3  cents  on  Tues- 
day, and  4  cents  on  Saturday,  how  much  did  he  earn  ? 

7.  28329         25365 
+  7    +2    +2    +5    +2    +10    +3    +  7    +4    +5 


+J> 

+  2 

+  10 

9 

-7 

7 
-_5 

7 
-2 

8.       4        9       5       9         7       7       8     10     11      10 
-2-2-3-7     -5-2-3-7-2-5 


COMBINATIONS   TO   12 

4     I       * 


1 

i 

1.  Draw  a  line.     Cut  it  into  two  equal  parts.     What 
is  one  part  ? 

2.  Fold  your  paper  once  in  the  middle.     It  is  whut 
part  as  large  as  before  you  folded  it  ? 

3.  Point  to  one  half  of  the  circle  at  the  top  of  the  page. 

4.  Point  to  one  half  of  the  square  at  the  top  of  the  page. 

5.  One  half  of  4  cents  is  how  many  cents  ?     (Picture.) 

6.  Take  six  counters.     Find  one  half  of  them.     One 
half  of  six  are  how  many  ? 

7.  Find  one  half  of  eight;  of  10  ;  of  12. 

8.  Half    a   dozen   apples   at   a   cent   each   cost   how 
much  ? 

9.  George  bought  a  half  dozen  apples  and  gave  4  to 
Rose.     How  many  had  he  left  ? 

io.    4  days  and  how  many  days  make  a  week  ? 

li.    How  many  cents  in  a  half  dime  ? 

12.     2       4       3       2       6       3       2        10        12        11 
x3x2x3xox2x4x2       -3       -6       -5 


10  COMBINATIONS  OF   TWO 

i.  Make  6  marks.  Group  them  by  2's.  How  many 
2's  in  6  ?  Group  them  again,  showing  2  halves  of  6. 
One  half  of  6  is  how  many? 

2.  Do  the  same  with  8,  10,  12,  14,  16,  18,  20. 

3.  •  Read  42,  89,  76,  98,  73,100. 

4.  Read  I,  IV,  V,  III,  II. 

5.  Add: 

6653  4  25843 
2326411123 
3175432233 
2112243223 

6.  334289   10   325 
^^^x7x^x2x2x3x_3x2 

7.  2)6  3)6  2)1  2)8  2)10  3J9"  2)12  4JS 
a  3)12  4)12  5)To  3)15  6)12  2)13  7jl? 
9.    Find  J  of  6  cents ;  l  of  14  marbles  ;  \  of  8  birds. 

10.       4      5      7       2       8        2         2      14     10       5 
+  2   +2   +2    +4    4-2    +11    +13    +1    +2    +3 




— 

— 



ii.       5       8 

9 

5 

7 

7 

8 

11 

12 

11 

-2    -3    - 

4 

-3    - 

-4    - 

-3 

-5 

-5 

-6 

-6 

12.   Add: 

2       3       2 

4 

8 

7 

3 

2 

9 

1 

1       4       5 

3 

1 

2 

2 

1 

1 

2 

111 

1 

2 

3 

4 

2 

2 

3 

2       5       2 

2 

1 

1 

1 

4 

1 

6  - 

COMBINATIONS  OF   TWO 


11 


i.   VI  =  5  +  1*=6       VII  =  5  +  2  =  7       VIII  =  5  +  3  =  ? 

2.  X=10  IX=10-1  =  9  XI  =  10  +  1  =  11 

XII  -  10  +  2  =  ? 

3.  How  many  2-cent  stamps  would  cost  as  much  as 
a  1 2-cent  kite  ? 

4.  How  many  school  days  in  2  weeks?     How  many 
working  days  ?     How  many  days  in  all  ? 

5. 


What  did  the  stamps  on  these  letters  cost  ? 


6. 


7. 


Five  2's  are  how  many  ?     Six  2's  are  how  many  ? 
Write  in  Roman : 

The  number  of  cents  in  a  dime. 
The  number  of  feet  your  cat  has. 
The  number  of  pints  in  4  quarts. 
The  number  of  lemons  in  a  dozen. 
The  number  of  eggs  in  a  half  dozen. 
/.    The  number  of  days  in  a  week. 
g.    One  less  than  a  dozen. 

Grace  is  reading  Chapter  X  in  her  book  and  Frank 
is  reading  Chapter  VII.  Grace  is  how  many  chapters 
ahead  of  Frank  ? 


a. 
b. 
c. 
d. 
e. 


8, 


12 


COMBINATIONS  OF   TWO 


i.    Count  these   dots   by   2's:    IJt4 ••••*•••• 

How  many  2's  are  there  ?  How  many  dots  are  there  in 
the  upper  row  ?  In  the  lower  row  ?  Twelve  dots  are 
what  part  of  24  dots  ? 

2.  Make  dots  to  show  two  2's ;  three  2's ;  four  2's ; 
five  2's;  seven  2's;  nine  2's;  six  2's;  eleven  2's. 

3.  How  many  2's  are  there  in  4  ?     In  8  ?     In  10  ? 
In  14?     In  20?     In  22  ?     In  16?     In  24  ?     In  6? 

4.  Show  that  there  are  two  12's  in  24,  thus, 

=  12 

=  12 

5.  Show  that  there  are  two  8's  in  16. 

6.  Show  how  many  tens  there  are  in  20. 

7.  This  domino  shows  that  6-4-6  = 
12,  that  12-6  =  6,  that  two  6's=12, 
that  six  2's  =12,  and  that  |  of  12  =  6. 

8.  This    domino    shows    that    5  + 

4  = ,  that   9  —  5  = ,   and   that 

9-4  = . 

9.    Tell  what  is  shown  by  each  of  these  dominos : 


•  •     •        • 

•  •     •        • 


•  •     •        • 

•  •     •        • 


•  •     •        • 

•  •     •        • 


•  •   •     • 

•  •   •  • 


io.        2       4       8       12       7       5 

+  2    +4    +8    +12    +7    +5 


•      •      • 

•             • 
• 

•     •      • 

•             • 

o 
3 

9       11       10 

+  3 

+  9   + 

11    4-10 

COUNTING    BY  2'S  13 

i.  count.  :  :  :  :  : 

1  3  5  7  9  11 
2.  9  and  2  are  how  many  ? 

3.  count. ::::::::::  19  +  2  =  ? 

4.  29  +  2  =  ?   39  +  2  =  ?   49  +  2  =  ?   59  +  2  =  ? 
69  +  2  =  ?  79  +  2=?  89  +  2  =  ?  99  +  2  =  ? 

5.  Count  by  2's  from  1  to  99. 

6.  Count  by  2's  from  99  to  1. 

7.  John    had   7  marbles  and  bought  6    more.     How 
many  had  he  then?     Show  by  a  picture. 

8.  7  +  6  =  ?     6  +  7  =  ?     13-6  =  ?     13-7  =  ? 

9.  Arthur  paid  8  cents  for  a  tablet  and  6  cents  for 
pens.  What  did  both  cost?     8  and  6  are  how  many? 

10.  William  had  14  cents.    He  paid  6  cents  for  a  quart 
of  milk.     How  many  cents  had  he  left  ?     (Picture.) 

11.  A  boy  found  14  eggs  in  a  nest  and  sold  a  dozen. 
How  many  were  left  ?     Show  by  a  picture. 

12.  Add : 
6266226211 
1  '  3  2  3  2  24332 
353173  1121 
2221122233 
1113581451 


13.    Subtract : 

4      5      8      11 

13 

9 

8 

10 

12 

13 

14 

15 

2      3      5        6 

7 

3 

2 

5 

_7 

6 

8 

_7 

14  PROBLEMS 

1.  A  year  and  3  months  are  how  many  months  ? 

2.  Our  baby  is  11  months  old.     How  old  will  he  be 
3  months  from  now  ? 

3.  A  dozen  and  three  oranges  are  how  many  oranges  ? 

4.  Make  dominoes  that  count  5,  7,  10,  9,  11. 

5.  A  dozen  and  4  eggs  are  how  many  eggs  ?     (Picture.) 

6.  Alice  is  16  years  old  and  Ethel  4  years  younger. 
How  old  is  Ethel  ? 

7.  James  picked  9   quarts  of  cherries  and  Donald  4 
quarts.     How  many  quarts  did  both  pick  ? 

8.  A  boy  earned  14  cents  and  gave  his  sister  11  cents. 
How  many  cents  had  he  left  ? 

9.  How  many  evening  papers  at  2  cents  apiece  will 
18  cents  buy  ? 

10.    How  many  shoes  in  10  pair?     In  12  pair? 
n.    Nine  robins  have  how  many  feet  ? 

12.  How  many  2's  in  14  ?     20  ?     22  ?     24  ?    18  ?    16  ? 

13.  Find  \  of  8  books;  of  12  pints;  of  16  cents;  of 
10  dollars. 

14.  Answer  each  of  these  questions  in  three  ways : 


?  +  ?=10 

?  +  ?= 

16 

? 

+  ?  = 

14 

?+?=15 

3-?  =    ? 

14-?  = 

? 

13 

-?  = 

? 

16-?=    ? 

17.   Add 

• 

6        6 

5 

3 

4 

3 

1 

7 

3         7 

2        3 

2 

6 

4 

5 

2 

3 

2         1 

3         1 

7 

2 

4 

2 

3 

4 

4         2 

2         1 

1 

5 

2 

1 

4 

6 

3         8 

YARD  AND  FOOT  15 

Note.  —  If  possible,  let  each  pupil  be  provided  with  a  yardstick.  At 
/east  have  several.  Let  pupils  have  much  practice  in  estimating  and  meas- 
uring. 

i.    Draw  a  line  1  yard  long  on  the  blackboard. 

2.  Find  something  in  the  room  a  yard  long  or  wide. 

3.  How  long  do  you  think  the  schoolroom  is  ?     How 
wide  ?     Measure  it.     Find  something  1  yard  high. 

4.  Name  some  things  that  are  always  measured  by  the 
yard. 

5.  Without  the  yardstick  draw  a  line  one  yard  long. 
Measure  and  correct  it.     A  line  2  yards  long. 

6.  How  long  do  you  think  the  blackboard  is  ?     Meas- 
ure it,  and  see  how  nearly  correct  your  estimate  is. 

7.  Hold  your  hands  1  yard  apart.     Hold  them  1  yard 
above  the  floor. 

Note.  —  yd.  stands  for  yard  or  yards. 

8.  What  will  2  yd.  of  ribbon  cost  at  7  cents  a  yard  ? 

9.  How  many  yards  of  ribbon  will  22  cents  buy  at 
2  cents  a  yard  ? 

10.  Draw  a  line  1  yd.  long.  Divide  it  into  3  equal 
parts.     What  is  one  of  these  parts  ? 

n.  Hold  your  hands  one  foot  apart.  Draw  a  line  1  foot 
long.     Hold  your  hand  one  foot  above  your  desk. 

12.  How  many  feet  high  are  you  ? 

13.  Without  a  rule  draw  a  line  2  feet  long.  Measure 
and  correct  it.  Do  the  same  with  lines  3,  4,  5,  and  6  feet 
long. 


16  THREE 

i.    How  many  feet  are  there  in  2  yd.  ?     In  3  yd.  ?     In 
4  yd.  ?     In  5  yd.  ? 

Note. — ft.  stands  iorfoot  or  feet. 

2.  How  many  yards  in  15  ft.  ? 

3.  A  line  6  yd.  long  is  how  many  feet  long  ? 

4.  A  line  6  ft.  long  is  how  many  yards  long  ? 

5.  Count  by  3's  from  0  to  24  and  back  to  0. 

6.  Two  3's  are  how  many  ?    Four  threes  ?    Seven  3's  ? 
Six  3's?     Three  3's?     Five  3's?     Eight  3's? 

7.  Nellie's  father  is  6  ft.  tall.     His  height  is  the  same 
as  how  many  yards  ? 


a 

beven  yard 

Is  01  cl< 

oth  are 

ikm 

v  many 

lei 

et  li 

ongT 

9. 

7  +  3  =  ? 

9-t 

-3  =  ? 

12 

+  3  = 

=  ? 

13  +  3  =  ? 

10. 

5-3  =  ? 

11- 

•3  =  ? 

8 

-3  = 

=  ? 

9-3  =  ? 

n. 

Add: 

4 

4         3 

4 

2 

3 

4 

5          7 

3 

6         5 

7 

1 

4 

6 

1          2 

5 

3         3 

3 

3 

2 

3 

2          3 

3 

12. 

3         7 

Subtract  : 

2 

4 
3 

1 
1 

1 

2 

3          1 

1          4 

13 

12       15 

16 

11 

11 

12 

10 

9       10 

7 

6         3 

_4 

_9 

2 

3 

_T_ 

5      J 

13. 

8 

Multiply  : 
3         4 

11 

12 

9 

10 

3 

2        7 

2 

5         3 

2 

2 

2 

2 

3 

4        3 

14.    DimVfe;  2)6     3)6     4)12     3)12     3)15     8)16     2)14 


ONE  THIRD  17 


i.    Divide  a  yard  into  feet.     One  foot  is  what  part  of 
a  yard  ?     One  third  of  3  ft.  is  how  many  feet  ? 

2.  One  third  of  6  cents  are  how  many  cents  ?  2  !  2  i  2 

3.  How  many  3's  in  6  ?     $  of  6  =  ?     §§§ 
How  many  2's  in  6  ?     $  of  6  =  ? 

4.  J  of  9  feet  are  how  many  feet  ? 

5.  ^  of  3  yd.  are  how  many  yards  ? 

6.  Three  3's  are  how  many  ? 

7.  ^  of  9  dots  are  how  many  dots  ? 

8.  How  many  3's  in  9  ? 


•  •  • 

•  •  • 

•  •  • 


9.    IJour  times  3  are  how  many  ? 


•  •  • 

•  •  • 


10.  How  many  3's  in  12  ?     1  of  12  =  ?         HI 

11.  A  ribbon  12  ft:  long  is  how  many  yards  long  ? 

12.  Five  3's  are  how  many  ?     Show  this  by  a  picture. 

13.  |  of  15  =  ?     How  many  3's  in  15  ? 

14.  Six  3's  are  how  many  ?  ^  of  18  =  ?  How  many  3's 
in  18  ?     Show  this  with  dots. 

15.  An  orchard  has  3  rows  of  trees  with  8  trees  in  a 
row.  How  many  trees  in  the  orchard  ?  Make  a  picture 
of  it. 


18  GALLON 

Keep  the  measures  before  the  class. 

1.  What  measures  are  these? 
For  what  is  the  quart  measure 
used?  For  what  is  the  gallon 
measure  used  ? 

2.  Fiji  the  quart  measure  with 
water.  Pour  it  into  the  gallon  measure.  Repeat  till  the 
gallon  measure  is  full.  How  many  times  did  you  empty 
the  quart  measure?  How  many  quarts  make  a  gallon 
(gal.)  ?     Write  on  the  blackboard  what  you  have  learned. 

3.  How  many  quarts  in  2  gallons  ?     In  3  gallons?     In 
6  gallons  ?     In  5  gallons  V     In  4  gallons  ? 

4.  How  many  pints  in  1  gallon?     In  2  gallons? 

5.  A  gallon  of  milk  costs  how  much   at   5   cents  a 
quart  ? 

6.  Two  quarts  were  spilled  from  a  gallon   of   water. 
How  much  remained? 

7.  What  must  I   pay  for  a   gallon  of  vinegar   at  6 
cents  a  quart  ? 

8.  Eight  quarts  are  equal  to  how   many  gallons?    16 
qt.  ?  24  qt.  ? 

9.  Count  by  4's  from  0  to  24 ;  from  1  to  13 ;  from  2 
to  18;  from  3  to  15 ;  from  2  to  26. 

10.  -|  of  4  qt.  are  how  many  quarts  ?  How  many  quarts 
in  a  half  gallon  ? 

li.    Count  by  3's  from  1  to  37 ;  from  2  to  38. 

12.  Count  by  2's  from  0  to  50  and  back ;  from  1  to  51 
and  back. 


TWO,   THREE  AND  FOUR  19 

1.  9  +  2  =  ?     19+2  =  ?     29  +  2  =  ?     39  +  2  =  ? 

2.  11-2  =  ?     21-2  =  ?     31-2  =  ?     41-2  =  ? 

3.  When  you  buy  5  quart  bottles  and  2  pint  bottles  of 
milk,  how  many  quarts  do  you  get  ? 

4.  234353246 
+  2     +2     +1     +4     +2     +4     +3     +2     +2 

5.  754768656 
-2     -4     -2     -4     -3     -3     -1     -4     -4 

6.  XIII  =  10  +  3  =  13.     XIV  =  10  +  4  =  ? 

7.  Express  13  and  14  in  Roman  notation. 

8.  Copy  in  figures  and  give  answers : 

III  +  II  =  ?     V-III  =  ?    V-II  =  ?  IY  +  VIII  =  ? 

V  +  III  =  ?    II  +  X  =  ?      V  +  VII  =  ?  VIII  +  V  =  ? 

9.  3        4        3        4        4        2  12       10      11 
x6      x4      x8     x6      x5      x8  x2      x2     x2 

10.  4)12     3)15     4)20     3)21     4)24    4)16    4)l2    3)18 

n.  XV  =  10  +  5  =  15.     XVI  =  10  +  6  =  ? 

12.  Express  in  Roman  all  the  numbers  to  16. 

13.  Copy  in  figures  and  give  answers: 

V  +  V  =  ?        VIII  +  IV  =  ?        III  +  IX  =  ? 

14.  Add:  15.    Subtract: 
46324  697548 
11232            233245 
34424 

16.    Count  by  3's  from  1  to  22. 


20 


ONE  FOURTH 


i.  How  many  fourths  are  there  in  the  square  ?    In  the 
line  ?     In  the  circle  ?     In  the  orange  ? 

2.  Draw  a  foot  line  and  divide  it  into  four  equal  parts. 
What  is  each  part  called  ? 

3.  One  quart  is  what  part  of  a  gallon  ? 

4.  One  fourth  of  8  is  how  many  ?     J  |  J  |  J  |  J 

5.  Show  with  dots  J  of  12  ;   of  20 ;    of  16 :   of  24. 

6.  How  many  3's  in  12  ?     How  many  4's  in  12  ? 

7.  How  many  4's  in  20  ?     How  many  5's  in  20  ?     How 
many  4's  in  24  ?     How  many  6's  in  24  ? 

8.  How  many  are  three  4's  ?     Four  5's  ?     Four  6's  ? 

9.  If  a  pound  of  candy  costs  20  cents,  what  does  \  of 
a  pound  cost  ? 

10.    16  +  4  =  ?    8-2  =  ?    Jof8  =  ?    £ofl6  =  ? 

n.    XVII  =  10  +  7  =  17.  XVIII  =  10+   8  =  ? 

XIX  =  10  +  9  =  19.  XX  =  10  + 10  =  ? 

12.    Write  in  figures :  I;   III;  V;  X;   IX;  XI;  VIII; 
XIII;  XV;  XIV;  XII;  II;  VI;  VII;   XVI;  XX. 

Note.  —  Enlarge  and  fix  the  idea  of  fourth  by  having  papers  cut  in 
various  forms,  and  then  cut  or  folded  into  fourths. 


FIVE  21. 

i.    Count  by  5' s  to  50  and  back  ;  from  1  to  36  and  back. 

2.  A  nickel  is  equal  to  a  half  dime.     Two  nickels  are 
the  same  as  how  many  cents  ? 

3.  Three  lives  are  how  many  ?     Seven  fives  ? 

4.5  +  4  =  ?      4  +  5  =  ?    9-4  =  ?    9-5  =  ?    5+?  =  7 

5.  5  +  5  =  ?    10-?=5    6  +  5  =  ?    8  +  5  =  ?    7  +  5=? 

6.  Give  answers  in  Roman  :  Two  fives  =  ?    Four  5's=  ? 
7  +  2  =  ?     6  +  6  =  ?     5  +  5  =  ?     9  +  2  =  ?     10  +  2  =  ? 

7.  How    many   school   days  are  there  in  one  week  ? 
Three  weeks  ?     Four  weeks  ?     Six  weeks  ?     Five  weeks  ? 

8.  How  many  working  days  in  4  weeks?     In  1  week? 
In  3  weeks  ?     In  2  weeks  ? 

9.  How  do  you  find  \  of  anything  ?     \  ?     \  ?     \  ? 

10.    Draw  a  line  and  divide  it  into  5  equal  parts.    What 
is  one  of  these  parts  ? 
n.   What  is  i  of  10  ?     Of  20  ?     Of  25  ?     Of  15  ? 

12.  Count  by  3's  from  1  to  37  ;  from  2  to  35. 

13.  Find  \  of  18  ;  \  of  6  ;  \  of  12  ;  \  of  22  ;  \  of  15. 

14.  Find  \  of  24;  \  of  12;  \  of  6;  \  of  16;  \  of  15. 

15.  How  many  cents  had  Dick  when  he  had  earned  5 
cents  and  his  father  had  given  him  a  nickel  ? 

16    Nina's  bank  contained  13  cents  and  she  took  out 
a  half  dime.     How  much  remained  ? 

17.    Jack  had  3  cents.     How  much  more  did  he  need  to 
buy  a  10-cent  ball  ? 
is.    9  +  5  =  ?   10  +  5  =  ?   12  +  5  =  ?   11  +  5  =  ?   13  +  5  =  ? 


22  FOOT  AND  INCH 

i.  With  a  rule,  draw  a  line  one  foot  long.  Divide  it 
into  12  equal  parts.  What  is  one  of  these  parts  ?  How 
many  inches  make  one  foot?  (in.  stands  for  inch  or 
inches.) 

2.  Divide  the  foot  line  into  halves.  How  many  inches 
in  one  half  of  a  foot  ? 

3.  Divide  the  foot  line  into  thirds.  How  many  inches 
are  ^  of  a  foot  ?  -^  of  12  inches  are  how  many  inches  ? 
Four  is  what  part  of  12?     How  many  4's  in  12? 

4.  Divide  the  foot  line  into  4  equal  parts.  What  part 
of  a  foot  is  one  of  these  equal  parts  ?  How  many  inches 
in  J  of  a  foot  ?  How  many  3's  in  12  ?  What  part  of  12 
inches  is  3  inches  ? 

5.  How  many  inches  in  2  ft.  ?     2x12  =  ? 

6.  A  foot  and  2  in.  are  how  many  inches  ? 

7.  A  foot  and  3  in.  are  how  many  inches?  A  foot 
less  3  in.  ?     Hold  your  hands  3  in.  apart ;  6  in. ;  10  in. 

8.  How  many  inches  wide  do  you  think  your  desk  is  ? 
Measure  it  and  see. 

Note.  —  Have  much  estimating  and  measuring  to  fix  ideas. 

9.  A  chalk  box  is  8  in.  long  and  4  in.  wide.  How 
many  inches  of  string  would  reach  around  it  ? 

io.  How  many  inches  around  an  inch  square  ?  A  2-inch 
square  ?  A  3-inch  square  ?  A  4-inch  square  ?  A  5-inch 
square  ?     A  6-inch  square  ?     Draw  these  squares. 

n.  How  many  feet  in  24  inches  ?  12  inches  are  what 
part  of  24  inches  ? 

12.    Count  by  3's  to  36.     How  many  3's  in  36  ? 


FIVE 


23 


mu) 

1  Q^tf  ufj£(L£ 

30 ! L— 

-t'/  a  pml 

bJ    '  «&L, 

JwBfsi 

^■^^» m»-^ 

mfm 

^^^te^^, 

^^s=-— -    - 

1.  This  picture  shows  9  girls  and  their  teacher,  starting 
for  the  park,  which  is  12  miles  from  the  city.  The  car 
passes  through  a  village  7  miles  from  the  city.  That  is 
how  far  from  the  park  ?  Draw  a  line  to  show  the  railroad, 
and  make  crosses  on  it  to  show  the  city,  village,  and  park. 

2.  Each  seat  in  the  car  will  hold  5  persons.  Count  by 
5's  and  find  how  many  persons  can  be  seated  in  the  car. 

3.  How  many  seats  were  needed  for  this  party  ? 

4.  How  many  persons  will  6  seats  hold  ? 

5.  At  the  village  5  more  girls  joined  the  party.  How 
many  girls  were  there  in  the  party  then? 

6.  The  fare  from  .the  village  to  the  park  is  5  cents. 
How  many  cents  did  the  5  girls  pay  ? 

7.  How  many  fares  would  2  dimes  pay  ? 

8.  The  entire  trip  was  made  in  1  hour.  How  many 
miles  did  the  car  go  in  a  half  hour  ? 

9.  Mary  had  14  cents  to  use  at  the  park.  She  bought 
a  bag  of  peanuts  for  a  nickel  and  some  candy  for  4  cents 
What  did  she  pay  for  all  ?     How  much  had  she  left  ? 


24  SIX 

1.  Count  by  6's  from  0  to  24 ;  from  2  to  20 ;  from  3 
to  21 ;  from  5  to  23 ;  from  4  to  22. 

2.  How  many  working  days  in  2  weeks  ?    In  4  weeks  ? 
In  3  weeks  ?     In  5  weeks  ? 

3.  Count  by  6's  from  24  to  0. 

4.  Julia  bought  a  tablet  for  6  cents.     She  gave  the 
clerk  a  dime.     How  much  change  should  she  receive  ? 

5.  Sarah  is  12  years  old.     Mary  is  6.     What  is  the 
difference  between  their  ages  ? 

6.  If  Grace  is  6  years  older  than  Sarah,  how  old  is 
Grace  ? 

7.  What  must  be  paid  for  a  slate  worth  a  dime  and  a 
picture  worth  6  cents  ? 

8.  How  many  papers  must  Frank  sell  at  2  cents  apiece 
to  get  10  cents  ? 

9.  Eleven  marbles  and  six  marbles  are  how  many  ? 

10.    If  you  can  buy  6  marbles  for  a  cent,  how  many  can 
you  buy  for  4  cents  ? 

n.    Twelve  is  what  part  of  24  ?     6  is  what  part  of  24  ? 

12.  Six  inches  are  what  part  of  a  foot  ?     3  inches  ? 

13.  Six  is  1  of  what  ?     ^  of  what  ?     1  of  what  ? 

14.  Add : 
6666626662 
6666265122 

666664537 

6612346C 

6    6    3    2    2    2    1 


SEVEN  25 


1. 

Count  by  T 

s  fro 

m  0  to  28 ; 

from 

28  to  0. 

2. 

Add: 

7 

7        7 

7 

5 

7 

6 

7 

4 

1 

7 

7        7 

3 

2 

5 

2 

3 

7 

9 

7        7 

4 

6 

7 

3 

7 

2 

3 

7 

2 

7 

3 

.    7 

1 

7 

7 

3. 

Midtiply : 

7 

7        7 

6 

5 

3 

5 

3 

2 

4 

2 

3         4 

4 

6 

6 

4 

5 

7 

4 

4. 

Subtract  : 

7 

9       11 

14 

19 

16 

12 

13 

10 

15 

7 

7       __7 

J7 

__7 

J_ 

J_ 

_7 

J7 

J7 

5 

7)14     7)28 

7)21     \ 

iyf  3)i5 

3)18 

6)18 

4]2i 

6. 

Add: 

'7 

2         2 

7 

t 

7 

6 

7 

5 

7 

7 

2         2 

3 

4 

5 

3 

3 

7 

6 

4 

7         7 

3 

3 

3 

2 

3 

2 

5 

3 

2         6 

6 

4 

2 

7 

3 

2 

4 

7.    Count  by  7's  from  1  to  29 ;  from  5  to  26. 
s.    17-7  =  ?     19-7  =  ?     19-12  =  ?     7  +  ?  =  14 
9.    |  of  14  marbles  are  how  many  marbles  ? 
10.    7  is  J  of  what  number  ?     \  of  what  ? 

'    n.    How  many  days  are  there  in  2  weeks  ?     In  3  weeks  ? 

In  4  weeks  ?     A  week  is  what  part  of  21  days  ? 


26  EIGHT 

i.    Count  by  8's  to  24.     8  +  8  +  8  =  ?     Three  8's  are 
how  many? 

2.  8  +  8  =  ?     16-8  =  ?     8  +  ?  =  16.     16  +  ?  =  24. 

3.  What  is  J  of  24?     How  many  8's  in  24? 

4.  8  cents  and  a  half  dime  are  how  many  cents?     A 
dime  and  8  cents?     8  cents  and  what  make  a  dime? 

5.  A  dozen  pencils  are  how  many  more  than  8? 

6.  How  many  quarts  in  a  gallon?     How  many  pints 
in  a  quart?     How  many  pints  in  a  gallon? 

7.  How  many  pints  in  2  gallons?     In  3  gallons? 

8.  A  dozen  and  8  lemons  are  how  many  lemons? 
9.    Draw  on  the  blackboard  a  figure  like 

this,  making  it  10  inches  long  and  8  inches 
wide.     How  many  inches  across  both  ends? 


Across  both  sides?     Across  one  end  and  one  side? 
io.    10  +  10  =  ?     8  +  8  =  ?     10  +  8  =  ?     18-10  =  ? 

11.  Mary  is  11  years  old  and  Helen  8.     What  is  the 
sum  of  their  ages?     11  +  8  =  ?     19-11  =  ?     19-8  =  ? 

12.  Dorothy  is  11  years  old  and  Helen  7.     What  is  the 
sum  of  their  ages?     18-7  =  ?     18-11  =  ?     ?  +  ?=18. 

13.  A  foot  and  7  inches  are  how  many  inches?     A  foot 
and  9  inches?     A  foot  and  11  inches?     A  foot  and  10 


inches? 

14.       13 

15 

16 

17 

23 

21 

18 

17 

-8 

-7 

-8 

-9 

-11 

-11 

-10 

-10 

is.  3)24      6)24      12)24      8)24      4)24      6)12      2)16 


COMBINATIONS  TO  24  27 

1.  My  rule  is  2  feet  long.     How  many  inches  long  is  it  ? 

2.  14  oranges  are  how  many  more  than  a  dozen  ? 

3.  Harry  visited  his  uncle,  15  miles  from  Harry's  home. 
He  rode  12  miles  and  walked  the  rest  of  the  way.  How 
far  did  he  walk  ? 

4.  Willie  had  16  marbles  and  lost  4.  How  many  had 
heleft?     16-4  =  ?     12  +  12  =  ?     12x2  =  ?     14-12  =  ? 

5.  12  cents  and  a  half  dime  are  how  many  cents  ? 

6.  A  half  dozen  cakes  are  how  many  cakes?  How 
many  are  a  dozen  and  a  half  dozen  ?    12  +  6  =  ?    12  +  5  =  ? 

7.  Jennie  had  2  dimes.  How  many  cents  had  she  ? 
She  bought  a  pad  for  8  cents.  How  many  cents  had  she 
left?     20-8  =  ?     12  +  8  =  ?     20-12  =  ? 

8.  To-day  is  the  12th  day  of  the  month.  A  week  from 
to-day  is  what  day  of  the  month  ?  12  +  7  =  ?  19  -  12  =  ? 
19-7  =  ? 

9.  Ralph  has  21  chickens;  9  of  them  are  white  and 
the  rest  are  brown.     How  many  are  brown  ?     21  —  9  =  ? 

10.    A  dime  and  12  cents  are  how  many  cents  ? 

n.    A  foot  and  11  inches  are  how  many  inches  ? 

12.    Add : 

11 

4 

2 

2 


13. 


4 

9 

3 

6 

3 

2 

5 

6 

5 

2 

2 

5 

4 

4 

5 

2 

3 

1 

7 

6 

5 

6 

5 

3 

6 

9 

12 

5 

12 

3 

5 

6 

17 

16 

21 

23 

19 

18 

15 

13 

-9 

-7 

-11 

-12 

-11 

-12 

-9 

-7 

28  COMBINATIONS   TO  24 

i.   XXI  =  10  +  10  +  1  =  21     XXII  =  10  +  10  +  2  =  ? 
XXIII=  10  +  10  +  3  =  23     XXIV  =  10  +  10  +  4  =  ? 

2.  Write  in  Roman  all  the  numbers  to  24. 

3.  6  gallons  of  cream  are  how  many  quarts  ? 

4.  24  cents  will  buy  how  many  8-cent  tablets  ? 

5.  24  peaches  are  how  many  dozen  ?     (Picture.) 

6.  How  many  pints  of  milk  in  12  quarts? 

7.  A  rule  is  2  ft.  long.     How  many  inches  long  is  it  ? 
How  many  6-inch  pieces  would  it  make  ?     4-inch  pieces  ? 

8.  Add : 

884  12  11  2854 

712  3  32425 

316  2  49366 

285_3J8235 

9.  8  2        3         2        4        8       12        5        6 
x3      xll      x8     x8     x6      x2      x2      x4      x3 


10.    Multiply  : 
6           6           6 

5 

4 

4 

8 

9 

3 

3           4 

5 

4 

3 

5 

2 

2 

5 

11.   Add  : 

5           2 

2 

2 

1 

2 

2 

2 

5 

6           2 

2 

9 

5 

5 

5 

2 

2 

3           5 

8 

4 

7 

5 

5 

5 

10 

2          7 

5 

1 

3 

6 

4 

9 

10 

12.   5)25     5)20     5)10     4)20     3)15    2)10    5)15    6)12 


COMBINATIONS  TO  24 


29 


1.  How  many  tenpins  are  there  in  this  game?  They 
were  set  in  2  rows ;  how  many  were  there  in  each  row  ? 

2.  If  they  were  set  in  3  rows,  how  many  would  there 
be  in  each  row  ?  (Picture  it.)  If  they  were  set  in  4  rows  ? 
(Picture.)     If  they  were  set  in  6  rows  ?     (Picture.) 

3.  Each  boy  has  four  plays.  Charles  puts  down  3?  7, 
5,  2.     James  puts  down  8,  6,  4,  2.     Which  wins  ? 

4.  Here  is  the  score.      Find  who  wins  in  each  game. 


a. 


James 

Charles 

James 

Charles 

James 

Charles 

8 

9 

b. 

8 

2 

c. 

6 

4 

3 

5 

5 

2 

2 

6 

5 

2 

7 

3 

4 

3 

2 

3 

3 

12 

6 

4 

7 

6 

e. 

6 

4 

/• 

10 

11 

3 

4 

7 

11 

3 

0 

2 

8 

3 

5 

1 

0 

7 

2 

5 

2 

10 

11 

Note.  —  Play  more  games,  varying  them. 


30  COMBINATIONS   TO  24 

i.  Helen  has  a  half  dime.  May  has  3  times  as  much. 
How  much  money  has  May  ?     How  much  have  both  ? 

2.  Jennie  earned  14  cents  and  paid  a  dime  for  note 
paper.     How  much  had  she  left  ? 

3.  Divide  20  cents  among  4  girls.  How  much  does 
each  get  ? 

4.  A  dime,  a  half  dime,  and  2  cents  are  how  many 
cents  ? 

5.  How  many  shoes  do  9  children  wear  ? 

6.  If  a  lady  writes  one  letter  a  day,  what  do  her  postage 
stamps  for  a  week  cost  ? 

7.  How  many  candles  are  there  in  3  boxes  if  each  box 
holds  six  ? 

8.  How  many  feet  in  8  yards  ? 

9.  In  a  rose  bed  are  3  rows  of  bushes,  with  8  bushes 
in  each  row.  (a)  How  many  rosebushes  in  the  bed? 
(Picture.)  (b)  How  many  bushes  in  2  of  the  rows?  If 
there  were  4  rows,  how  many  bushes  would  there  be  in 
each  row  ?     (Picture.) 

DRILL    TABLES 

Note.  —  The  drill  tables  on  page  31  contain  those  additions  and  sub- 
tractions that  require  most  repetition.  It  is  a  waste  of  time  to  repeat  com- 
binations that  are  perfectly  known. 

Copy  these  tables  on  the  blackboard  and  go  through  them  daily  as  a 
rapid  drill  exercise.  Vary  the  order,  sometimes  going  across  and  sometimes 
up  and  down.  Occasionally  let  pupils  take  turns  in  pointing  while  others 
answer. 

In  the  subtraction  table,  let  results  be  given  in  both  forms "4  from 

12  leaves  8  "  and  "  4  aud  8  are  12." 


DRILL  TABLES 


31 


See  note,  page  30. 


ADDITION  DRILL  TABLE 


9 

2 

7 

4 

12 

8 

9 

11 

3 

6 

5 

2 

11 

s8 

12 

7 

11 

12 

11 

12 

8 

4 

11 

5 

10 

5 

9 

12 

5 

8 

9 

5 

2 

12 

9 

11 

7 

4 

12 

11 

12 

11 

8 

12 

6 

3 

12 

6 

6 

7 

7 

6 

4 

3 

6 

9 

8 

5 

7 

11 

4 

7 

4 

11 

9 

5 

8 

9 

11 

8 

7 

10 

3 

8 

6 

5 

6 

4 

9 

7 

8 

9 

12 

11 

9 

12 

7 

6 

SUBTRACTION  DRILL  TABLE 


12 
4 

18 
9 

18 

7 

16 
8 

22 
12 

16 
9 

14 
11 

17 
9 

18 
12 

10 
6 

19 
9 

15 
9 

11 

8 

17 
5 

13 

7 

17 
11 

11 
4 

14 

7 

10 
4 

15 
11 

12 
9 

11 
5 

23 
12 

14 

9 

21 
11 

12 

7 

13 
4 

24 
12 

16 
11 

20 
12 

20 
11 

13 

8 

14 
12 

11 
2 

13 
11 

15 

8 

16 
12 

19 

7 

19 
11 

21 
12 

22 
11 

15 

12 

17 

7 

9 
4 

12 
8 

20 
9 

18 
11 

19 
8 

16 

7 

22 
10 

14 
3 

17 

8 

18 
6 

8 
5 

14 

8 

15 
6 

11 
3 

17 
12 

13 
6 

17 
6 

11 

7 

10 
5 

16 
6 

15 
4 

10 
3 

11 
6 

23 
11 

14 

5 

21 
10 

12 
5 

13 
9 

8 
3 

16 
5 

20 

8 

7 
4 

13 
5 

14 

2 

11 
9 

13 
2 

15 

7 

16 
4 

19 

12 

12 

6 

21 
9 

8 
4 

12 
3 

9 
6 

9 
5 

32  READING   AND   WRITING  NUMBERS 

1.  One  hundred  is  written  100 ;  two  hundred  is  written 
200 ;  five  hundred  is  written  500. 

Write  four  hundred ;  seven  hundred  ;  eight  hundred. 

2.  Read  300  ;  600  ;  700  ;  400 ;  200  ;  500 ;  900. 

3.  324  is  read,  three  hundred  twenty-four. 
642  is  read,  six  hundred  forty-two. 

Read  759;  483;  279;  585;  986;  361;  416;  313. 

4.  Write  four  hundred  twenty-one ;  three  hundred 
forty-nine ;  six  hundred  fifty-two  ;  one  hundred  forty-one  ; 
two  hundred  ninety-one ;  seven  hundred  sixteen ;  nine 
hundred  seventy-seven. 

5.  Six  hundred  nine  is  written  609. 
Eight  hundred  ten  is  written  810. 

Write  three  hundred  eight :  four  hundred  six ;  nine  hun- 
dred one ;  two  hundred  fifteen. 

6.  Read  749  ;  982  ;  507  ;  308  ;  701 ;  209  ;  685  ;  420. 

7.  Read  385  ;  769  ;  835  ;  429  ;  651 ;  910  ;  203  ;  519. 
a  Read  999;  807;  666;  342;  111;  405;  612;  711. 
9.   Read  359  ;  460  ;  580  ;  307  ;  222  ;  809  ;  980 ;  630. 

10.  Write  five  hundred  ninety ;  five  hundred  nine ;  nine 
hundred  forty-one;  three  hundred  sixty;  four  hundred 
six ;  eight  hundred  seventy ;  five  hundred  fifty-five. 

n.  The  right-hand  figure  is  called  units'  figure,  the 
second,  tens'  figure,  the  third,  hundreds'  figure. 

634  is  6  hundreds,  3  tens,  and  4  units. 

Tell  the  number  of  hundreds,  tens,  and  units  in  246  ; 
321;  245;  807;  650;  718;  320;  510;  408;  907. 


Written  ADDITION  33 

i.    Add  59  and  8. 

59  8  units  and  9  units  are  17  units. 

8  17  units  =  1  ten  and  7  units. 

g^  1  ten  and  5  tens  are  6  tens.     67 


2.    Add  68  and  96. 


68 

96 

164 


6  units  and  8  units  are  14  units. 
14  units  =  1  ten  and  4  units. 

1  ten,  9  tens,  and  6  tens  are  16  tens. 
16  tens  ==  1  hundred  and  6  tens.     164  Answer. 


Note.  —  Explanations  of  processes  in  addition,  subtraction,  multiplica- 
tion, and  division  should  not  be  dwelt  upon  unduly.  Yet  it  is  well  for 
children  to  see  how  results  are  obtained,  though  they  may  not  be  required 
to  repeat  an  intricate  analysis  of  the  operation. 

Add: 
3.  28       4. 36       s.  93       6.  29       ?.  43       a  78       9.  66 

4  7  8  9  9  3  8 


10. 

42 

8 

ii.96 
_9 

12.28 
3 

13.  46 

5 

14.29 
_6 

15.37 

_8 

16.42 

9 

17. 

86 
33 

.is.  42 
69 

19.96 
25 

20.  18 

73 

21.  16 

46 

22.  19 

43 

23.  86 

44 

24. 

35 

48 

25.  96 

57 

26.  98 
63 

27.  99 

34 

28.  10 

48 

29.  70 
30 

30.  52 

19 

31. 

87 
24 

32.85 

49- 

33.18 

14 

34.  17 

15 

35.  67 

24 

36.  45 

85 

37.  93. 

29 

34                                          ADDITION  Written 

Add: 

i.   a.  7     6.  5     c.  4     d.  2     e.  12    /.  22  g.  22    h.  12 

4         4         7         4         17         31  11         11 

3         6         2          6         30         42  33          11 

213  520^42124 

2.  a.  41  J.  51  c  41   <?.  51   6.  61  /.  72  g.   33 

13    42    20     62    33  80     55 

21    63    75     73    40  61     40 

13  12    32     80    54  53     61 

30         4  units,  6  units,  5  units,  and  8  units,  are units. 

45         23  units  = tens  and units. 

16         2  tens,  3  tens,  1  ten,  4  tens,  and  2  tens  are tens. 

34.         tens  = hundred  and tens.     123  Answer. 

4.  a.  15   6.  24   c.  17  d.   15   e.  54  /.  12  g.   19 

24  16    34     34    47  24     82 
35    33    23     26    32  16     41 

14  12    52     41    23  35     63 

5.  a.   22  b.   24  c   17  d.   15  e.   56  /.  17  g.   46 

43     33    26     25    34  25     20 

14    17    34    37    12  34    32 

37    26    43     12    29  40     55 

6.  a.  23  b.   14  c.   26   £  25   e.  46  /.  29  g.   92 

42    '  18    13     43    34  41     8 

25  22    47     58    55  32     31 
12     14    12     64    42  68     40 


Oral  ADDITION  35 

1.  Find  the  whole  cost  of  a  pencil  at  5  cents,  a  tablet 
at  8  cents,  and  a  stamp  at  2  cents. 

2.  5  cents,  2  cents,  4  cents,  and  12  cents  are  — —  cents. 

3.  If  a  peach  cost  2  cents,  an  orange  6  cents,  and  a 
pineapple  12  cents,  they  all  cost  — ■ —  cents. 

4.  Add  2  to  9  ;  19  ;  29  ;  39  ;  49  ;  59  ;  69  ;  79  ;  89  ;  99. 

5.  Add  3  to  8  ;  18 ;  28 ;  38  ;  48  ;  58  j  68  ;  78 ;  88 ;  98. 

6.  7  +  4  =  ?   17  +  4  =  ?   27  +  4  =  ?   37  +  4  =  ?   47  +  4  =  ? 

7.  7  +  5  =  ?   17  +  5  =  ?   27  +  5  =  ?   37  +  5  =  ?    57  +  5  =  ? 

8.  Add: 

7       17       27       37       47       57       67       77       87       97 

$.    Count  by  3's  from  0  to  30 ;  from  1  to  31 ;  from 
2  to  32. 

10.    Count  by  4's  from  0  to  40 ;  from  1  to  37 ;  from 
2  to  38. 

n.  Count  by  2's  from  50  to  0 ;  from  49  to  1. 

v>.  Count  by  5's  from  1  to  31 ;  from  3  to  33. 

13.  Count  by  6's  from  30  to  0 ;  from  5  to  29. 

14.  Count  by  6Js  from  1  to  31 ;  from  3  to  27. 

15.  Count  by  7Js  from  0  to  35;  from  1  to  29 ;  from 
2  to  30. 

16.  A  kite,  an  orange,  a  ball,  and  a  top  each  cost  5  cents 
How  much  did  all  cost  ? 


36  ADDITION  Oral 

i.    Add : 


7 

17 

37 

47 

57 

67 

77 

87 

27 

7 

7 

7 

7 

7 

7 

7 

_7 

_7 

2. 

7 

17 

27 

37 

47 

57 

77 

87 

67 

9 

9 

9 

9 

9 

9 

9 

9 

9 

3. 

7 

17 

57 

87 

67 

37 

47 

27 

77 

8 

_8 

8 

8 

8 

8 

8 

_8 

8 

4. 

6 

16 

26 

46 

36 

86 

56 

76 

66 

5 

_5 

_5 

5 

5 

5 

5 

5 

5 

5. 

6 

16 

56 

86 

96 

5 

15 

85 

45 

4 

4 

4 

4 

4 

_5 

5 

5 

5 

6. 

6 

16 

26 

36 

56 

86 

66 

46 

76 

6 

6 

6 

6 

6 

6 

6 

6 

6 

7. 

6 

16 

26 

36 

46 

86 

56 

66 

76 

7 

7 

J_ 

J_ 

7 

7 

_7 

7 

7 

8. 

6 

16 

36 

86 

56 

76 

66 

46 

26 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9. 

6 

16 

36 

56 

26 

86 

46 

76 

66 

8 

8 

8 

8 

8 

8 

8 

_8 

8 

10. 

5 

15 

25 

35 

85 

75 

45 

65 

55 

6 

_6 

6 

_6 

6 

6 

6 

6 

6 

11. 

5 

15 

35 

65 

85 

75 

45 

25 

55 

7 

J_ 

J_ 

_7 

7 

7 

_7 

7 

j 

Written  ADDITION  37 

i.   Add : 

24  ]  The  numbers  added  are  addends. 

12  I    a  7  7     -J        The  result  of  addition  is  the  sum. 
36  f 

Note.  —  In  adding,  do  not  repeat  the  figures.    In 


14  J 

86  Sum         exaraPlel>saM 


4,  10,  12,  16. 
2,  5,  6,  8. 


2.  a.   12  b.   23  c.   24  d.   37  e.   97  /.  54  g.   61 

36  27  58  35  35  33  32 

24  45  32  46  56  25  45 
15  56  46  25  87  29  37 

3.  a.   13  b.   21  c.  33  d.   39  e.   83  /.  66  g.   98 

42  42  24  40  21  42  32 

25  31  44  8  40  81  43 
67  56  55  60  _9  38  37 

4.  a.   88  6.  66  c.  99  d.   22  e.  90  /.  42  g.   98 

42  42  88  39  88  66  21 

36  91  32  42  19  37  32 

77  33  41  ^0  18  41  14 

5.  a.  62  b.   22  c.  32  d.   33  e.   21  /.  61  g.   64 

14  44  45  25  15  28  38 

28  91  16  40  17  33  21 

33  18  94  28  83  25  45 

6.  a.   22  I.   39  c   29  d.   88  e.   96  /.  24  g.   81 

33  41  38  64  38  86  28 

44  80  50  49  80  19  72 

55  16  96  82  19  81  19 


38  ADDITION  Oral 

l.    Add : 


5 

15 

25 

65 

85 

55 

75 

35 

45 

9 

_9 

9 

9 

9 

9 

9 

_9 

9 

:.  5 

15 

85 

75 

25 

55 

35 

65 

45 

8 

8 

8 

_8 

J8 

J5 

8 

8 

8 

:.  7 

7 

7 

7 

7 

7 

7 

74 

7 

4 

14 

34 

54 

84 

64 

44 

7 

24 

4.  4        4        4        4        3       13       23         7         7 
6162646        7       _7      _7       53       63 

5.  4 

7 

6.  4 

8 

7.  4 

9 

s.   3      13      23        8        8       73         8       83         8 
i      J*      _§.      i£      3£      _1      M       _1       63 

9.    3 


14 

24 

34 

44 

54 

84 

64 

74 

_7 

7 

7 

7 

_7 

_7 

7 

7 

8 

8 

54 

8 

64 

44 

8 

24 

14 

34 

8 

74 

8 

_8 

84 

_8 

14 

24 

34 

9 

9 

74 

9 

9 

9 

9 

9 

44 

54 

_9 

84 

64 

13 

53 

23 

73 

9 

9 

33 

9 

9 

9 

9 

0 

43 

83 

9 

63 

12 

32 

22 

52 

72 

9 

9 

9 

9 

9 

9 

9 

_9 

82 

62 

42 

io.    2 

n.    17+4  =  ?    48  +  5  =  ?    39  +  7  =  ?    56  +  8  =  ? 


Oral  ADDITION  39 

1.  Count  by  2's  from  0  to  50 ;  from  1  to  51. 

2.  Count  by  3's  from  0  to  51 ;  from  2  to  47. 

3.  Connt  by  4's  from  0  to  100;  from  2  to  102. 

4.  Count  by  4's  from  1  to  101 ;  from  3  to  103. 

5.  Count  by  5's  from  2  to  97 ;  from  1  to  101. 

6.  Mrs.  Smith  buys  a  pint  of  cream  every  day.     How 
many  quarts  does  she  buy  in  24  days  ? 

7.  One  half  of  a  foot  is  how  many  inches?     \  of  a 
foot?    \  of  a  foot?    \  of  a  foot?     (Picture.) 

8.  Five  gallons  of  milk  will  serve  how  many  customers 
if  each  takes  a  quart  ?     If  each  takes  a  pint  ? 

9.  Count  by  6's  from  0  to  96;  from  2  to  98;  from 
5  to  95. 

10.   Add: 
17       7       27        15        29        38        25        33        56 

JlI-IAJL-IJL-IJL 

li.  Count  by  7's  from  0  to  98 ;  from  4  to  95. 

12.  Count  by  7's  from  2  to  100  ;  from  5  to  96. 

13.  Go  through  the  addition  drill  table,  page  31. 

14.  Count  by  6's  from  1  to  97 ;  from  3  to  99. 

is.   Find  l  of  24;  i  of  24;  |  of  24;  J  of  24;  J  of  24. 

16.  Count  by  7's  from  1  to  99 ;  from  6  to  97. 

17.  Add: 
888888888 

19        27        35        46        92       75       43       54       28 


40  ADDITION  Written 

The  fourth  figure  in  a  number,  counting  toward  the  left, 
is  thousands'  figure.  9000  =  nine  thousand.  3000  =  three 
thousand.     6241  =  six  thousand  two  hundred  forty-one. 

1.  Read  2128;  4521;  7938;  8000;  8106;  2300;  5840; 
6007;  9017;  2307;  8111. 

2.  Write  five  thousand;  one  thousand  three  hundred 
sixty-seven ;  one  thousand  nine  hundred  nine  ;  four  thou- 
sand eight ;  two  thousand  ninety-three. 


Add  up,  then  down : 

3.  a.   324  b.   142 
132    353 

c.  612 
225 

d.   416 
527 

e.   423  /  324 
576    521 

4.  a.  351  6.  254  c.  341  d.  649  e.  894  /.  342 

460  165  205  427  783  643 

243  342  370  583  527  845 

5.  a.  786  b.  483  c.  213  d.  138  e.  923  /  238 

483  547  426  24  761  182 

765  592  325  805  302  302 

293  384  136  41  50  56 

6.  a.  314  b.  517  c.  514  d.  235  e.  216  /.  932 

280  281  283  415  31  18 

179  305  107  800  58  271 

250  490  920  70  814  526 

303  235  116  J9  _76  _32 

Read  the  addends  and  the  sums  in  the  above  examples. 


MONEY  41 

1.  100  cents  make  one  dollar.     We  write  it  $1.00. 
200  cents  make  two  dollars.     We  write  it  $2.00. 
500  cents  make  five  dollars.     How  would  you  write  it  ? 

2.  125  cents  make  one  dollar  and  25  cents.  We  write 
it  $1.25.  Seventeen  cents  is  written  $.17,  17  ct.,  or  17^. 
349  cents  make  three  dollars  and  49  cents.  We  write  it 
$3.49.  Six  cents  is  written  $.06,  6  ct.,  or  6£  Two  hun- 
dred twenty-five  cents  make  how  many  dollars  and  cents  ? 
How  would  you  write  it  ? 


3.   Read  $4.00 


4.  Read  $1.25 

5.  Read  $4.32 


.00;  $15.00;  $25.00;  $49.00 


,16. 


$.08. 
$.10. 

$.95. 


$2.25;  $4.35;   $6.23;  $17.53 
$7.50;  $8.40;    $1.05;   $16.10 

6.  Read  $27.20;  $8.07;  $3.01;  $2.10;  $30.01 

7.  Read  $2.52;  $1.37;  $2.49;  $3.65;  $4.03;  $81.20. 

8.  Read  the  numbers  in  question  i  as  cents. 

9.  Read  the  numbers  in  question  4  as  cents. 

10.    $2.43         Read   these   addends   as   cents,   then   as 
1.25     dollars  and  cents.     Add  them  and  read  the 


6.47 

sum. 

5.81 

6.35 

n.  Read  and  add : 

a.   $  4.23 

b.   $  .42 

c.  $3.81 

d.   $1.86 

e.  $2.35 

6.87 

1.37 

.59 

2.35 

4.16 

4.19 

.58 

.47 

4.81 

.89 

12.15 

.69 

.33 

7.63 

5.71 

8.52 

4.73 

4.44 

.48 

.60 

42 


ADDITION 


Oral 


l.   James  had   $.29  and   found   $.02.     He  then  had 
—  cents. 


2.  There  were  57  sheep  in  one  field  and  5  in  another. 
In  both  fields  there  were sheep. 

3.  How  many  pupils  in  a  class  composed  of  23  girls 
and  8  boys  ? 

4.  A  yard  of  cloth  cost  56  cents  and  a  yard  of  ribbon 
9  cents.     They  both  cost cents. 

5.  William  is  18  years  old  and  Frank  is  7.     The  sum 
of  their  ages  is years. 

6.  Two  fours  and  five  threes  make  how  many  ? 

7.  Add: 

36         49         36         42         38  64         85         39 

78596979 


PROBLEMS  43 

1.  There  are  26  pupils  in  one  class,  26  in  another,  and 
40  in  a  third.     How  many  pupils  in  the  three  classes? 

2.  A  farmer  raised  387  bushels  of  corn  the  first  year, 
293  the  second,  468  the  third,  and  99  the  fourth.  How 
many  bushels  did  he  raise  in  the  four  years  ? 

3.  A  boat  is  loaded  with  927  bushels  of  corn,  383 
bushels  of  wheat,  898  bushels  of  barley,  and  629  bushels 
of  oats.     How  many  bushels  in  the  load  ? 

4.  During  the  month  of  June,  the  meat  for  our  family 
cost  $7.18,  the  flour  $3.88,  the  butter  $2.79,  the  sugar 
$2.18,  and  the  rent  $25.     What  did  all  of  them  cost  ? 

5.  Our  lot  is  66  ft.  wide  and  168  ft.  long.  Make  a 
picture  of  it.     How  far  must  I  go  to  walk  around  it  ? 

6.  A  girl  paid  48  cents  for  stamps  and  37  cents  for 
postal  cards.     What  did  both  cost  ? 

7.  Write  and  add  : 

Seventy-eight  cents ;  two  dollars  and  seventy-nine  cents ; 
16  dollars  and  eight  cents ;  eighty-three  dollars  and  seven 
cents ;  thirty-one  dollars  and  sixteen  cents.  What  are 
these  numbers  called  ?     What  is  the  answer  called  ? 

8.  Henry  spent  47  cents  for  tea,  69  cents  for  potatoes 
and  93  cents  for  apples.    How  much  money  did  he  spend  ? 

9.  Shoes  for  $3.50,  a  hat  for  $2.50,  a  suit  of  clothes 
for  $17.75,  an  overcoat  for  $12.98  and  underwear  for 
$6.56  cost  in  all  how  much? 

10.  Sarah  had  $  .89  after  buying  a  50-cent  book  and  a 
25-cent  comb.     How  much  had  she  at  first  ? 


44  ADDITION  Oral  and  Written 

i.  7  +  7  +  3  +  8  = 2.  6  +  5  +  7  +  2  +  6  = 

6+8+6+2= 5+7+6+9+9= 


5+3+9+5= 4+6+8+7+4= 

8+9+7+7= 8+8+5+8+3= 

+  +  +  =   ?  +  +  +  +  = 

3.  9  +  6  +  5  +  6  = 4.  7  +  8  +  9  +  6  +  8  = 

4+7+8+3= 6+9+4+4+7= 

2+5+4+9= 9+5+3+5+5= 

8+4+7+5= 5+4+1+3+4= 

7+7+6+4= 3+3+7+8+8= 

+  +  +  =   ?  +  +  +  +  = 

5.  3  +  6  +  4  +  8  = 6.  9  +  3  +  8  +  10  +  5  =  — 

5  +  2  +  9  +  6  = 6  +  4  +  2+  4  +  8  =  — 

4  +  3  +  2  +  1  = 7  +  8  +  3+  9  +  2  =  — 

8  +  6  +  9  +  5  = 6  +  0  +  5+  7  +  3  =  — 

+  +  +  =   ?  +  +  ++  = 

7.  Add : 

a.  783      b.  492      c.  $6.07  d.  %  .96      e.  $12.10 

472            18               .49  4.71               3.19 

921            96               .63  5.83                 .29 

687          439             4.07  6.92             17.00 

432          897            _^21  _^88               6.31 

8.  a.  $   4.83       "6.  $8.49       c.  $19.07       d.  $   8.36 

.79              6.72  10.50                  .48 

6.85                .36  .18                   .90 

12.92              4.07  3.98                4.07 

13.07              5.60  7.62               16.00 


Oral  SUBTRACTION  45 

i.    Take  5  from  7;   13;  17;  15;  10;  9;  12;  11;  8. 

2.  Take  4  from  9;  11;  13;  16;  12;  7;   15;  10;  14. 

3.  There  are  11  seats  in  a  row.     Children  sit  in  all 
but  two  of  them.     How  many  children  in  the  row  ? 

4.  Take  3  from  8;  12;  9;  15;  13;  7;  10;  14;  11. 

5.  Take  7  from  9;   14;  16;  18;  13;  19;  15;  17;  11. 

6.  May  planted  39  rosebushes.     Two   of   them  died. 
How  many  lived  ?     Picture  them  in  3  rows. 

7.  Count  by  2's  from  49  to  1. 

8.  Take  11  from  15;  13;  17;  11;  21;  19;  22;  23. 

9.  Take  2  from  11;  21;  31;  51;  61;  81;  71;  41. 

10.  Take2froml0;  20;  30;  80;  90;  60;  40;  70;  50. 

11.  John  bought  some  raisins  for  12  cents  and  gave  the 
clerk  2  dimes.     How  much  change  should  he  receive  ? 

12.  Take6froml2;  14;  18;  9;  11;  17;  15;  16;  10. 

13.  Take  9  from  12;  10;  13;  15;  17;  18;  21;  19. 

14.  A  half  dime  and cents  make  17  cents. 

15.  Take  12  from  15;  18;  12;  24;  20;  23;  19;  21. 

16.  Take  10  from  20;  19;  22;  16;  21;  18;  15;  17. 

17.  Take8froml0;  9;  13;  20;  15;  19;  16;  18;  17. 

18.  Luther  and  John  earned  20  cents  shoveling  snow. 
John  earned  12  cents.    How  many  cents  did  Luther  earn  ? 

is.  8  +  7  =  ?   15-8  =  ?  15-7  =  ?  8  +  ?=17   7  +  ?=17 

20.  4  +  ?  =  12     ?  +  8  =  12     12-4  =  ?     12-8  =  ? 

2i.  + =  18.     + =15. 

22.  A  foot  less  7  inches  are  how  many  inches  ? 


46  SUBTRACTION  Written 

1.  From  378  take  135. 

378  Minuend         5  units  from  8  units  leave  3  units. 

135  Subtrahend     3  tens  from  7  tens  leave  4  tens. 

243  Remainder     1  hundred  from  3  hundreds  leaves  2  hundreds. 

The  number  from  ivhich  we  subtract  is  the  minuend. 

The  number  subtracted  is  the  subtrahend. 

The  result  of  subtraction  is  the  difference  or  remainder. 

2.  From  948  take  716.  Which  of  these  numbers  is 
the  minuend?  Which  is  the  subtrahend?  What  shall 
we  call  the  result? 

3.  836      4.  956      5.  507     6.  738     7,  89       8.  938 
-423         -25       -203       -607       -26         -817 

9.    769     10.  807    ii.  486    12.  985    13.  631    14.  639 
-553       -503       -375       -474       -420       -317 

15.    863     is.  347    17.  450    is.  892    19.  298    20.  847 
-751       -216       -320       -660       -162       -516 

21.  The    subtrahend    is    342    and   the   minuend    483. 
What  is  the  difference? 

22.  The  minuend  is  98  and  the  subtrahend  48.     Find 
the  remainder. 

23.  What  is  the  difference  between  837  and  206  ? 

24.  How  much  larger  is  984  than  863  ? 

25.  What  number  added  to  48  makes  89  ? 

26.  A  kite  string  897  feet  long  is  how  much  longer 
than  a  kite  string  492  feet  long  ? 


Oral  and  Written     ADDITION  AND  SUBTRACTION 


47 


2 

5 

8 

10 

7 

11 

3 

12 

6 

4 

9 

a.  Add  2,  3,  4,  5,  6,  7,  8,  9,  10,  11,  and  12  to  each  of 
the  numbers  in  the  squares. 

b.  Subtract   every  number   in   the   squares   from  14 ; 
from  15;  from  16;  from  17;  from  18. 

Add: 

2.     5       15       25       35       85       75       45       65       55 
666666666 


•— 

3.   5 

15 

35 

65 

85 

75 

45 

25 

55 

7 

J_ 

7 

7 

7 

7 

7 

7 

jr 

4.   2 

12 

32 

22 

52 

72 

9 

9 

9 

9 

9 

9 

9 

9 

9 

82 

62 

42 

5.  38 

99 

28 

85 

23 

92 

86 

49 

52 

74 

43 

95 

95 

87 

88 

78 

35 

71 

6.  How  much  farther  is  296  miles  than  85  miles  ? 

7.  A  bushel  of  apples  cost  %  1.25 
A  box  of  oranges  cost  4.35 
A  box  of  soap  cost  3.45 
A  dozen  cans  of  corn  cost  1.44 
They  all  cost 

8.  Find  the  difference  between  104  and  507. 

9.  $14.28       io.    $85.92       n.    $86.27       12.    $12.86 
-12.06  -15.70  -16.15  -9.10 


48  SUBTRACTION  Oral 

1.  30                     30  =  20  +  10 
-2  2= 2 

28  Difference  20+   8  =28     Difference 

2.  73  73  =  60  +  13 
-8  8=  8 


65  Difference  60  +   5  =  65     Difference 

3.  Subtract  2  from  10  ;  20  ;  30  ;  40  ;  50  ;  60  ;  70  ;  80. 

4.  Subtract  3  from  10  ;  20  ;  30 ;  40  ;  50  ;  60  ;  70  ;  80. 

5.  Subtract  4,  5,  6,  7,  8,  and  9  from  the  same  num- 
bers as  those  given  in  question  4. 

6.  Subtract  2  from  11,  21,  31,  41,  51,  61,  71,  81,  91. 

7.  From  the  same  numbers,  subtract  3,  4,  5,  6,  7,  8,  9. 

8.  12       22       32       42       52       62      72       82      92 
^^_2_2_2_2_2_2_2 

9.  Subtract  3,  4,  5,  6,  7,  8,  and  9  from  the  minuends 
given  in  question  8. 

io.      13       23       33       43       53       63      73      83      93 

li.    Subtract  4,  5,  6,  7,  and  9  from  the  minuends  given 
in  question  io. 

12.      14     24      94      14      24      34      44      54     64     74 


-4 

-4 

-4    - 

_5    _5    _5    _5    _5   _5 

-5 

13. 

84 

94 

14 

24       34       74      84      94 

14 

-5 

-5 

-6 

-6     -6     -6     -6     -6 

-7 

Written  SUBTRACTION  49 

i.  One  ten  =  how  many  units  ? 

2.  One  hundred  =  how  many  tens  ? 

3.  One  thousand  =  how  many  hundreds  ? 

4.  From  473  take  135< 

473  =  4  hundreds  +  6  tens  +  13  units. 
135  =  1  hundred  +3  tens  +    5  units. 


338  =  3  hundreds  4-  3  tens  +  8  units.     Difference. 

We  cannot  take  5  from  3.  So  we  take  1  ten  out  of  7  tens,  put  it 
with  3,  making  13  units,  and  subtract  5  units  from  13  units.  We 
then  take  3  tens  from  6  tens,  and  1  hundred  from  4  hundreds.  How 
do  -we  get  6  tens  ? 

5.  From  629  take  237. 

629  =  5  hundreds +  12  tens +  9  unitSo 
237  =  2  hundreds  +  3  tens  +  7  units. 
392  =  3  hundreds  +    9  tens  +  2  units. 

Can  you  tell  how  this  is  done?  How  do  we  get  12 
tens  ?     How  do  we  get  5  hundreds  ? 

6.  981      7.  352      a.  764     9.  662    10.  816    11.  236 
-732       -135       -545       -254       -623         -52 

12.    149     13.  918    14.  732    15.  608    is.  983    17.  536 
-56         -48       -313         -27       -874       -435 

is.    439    is.  906    20.  382    21.  641    22.  319    23.  709 
-247       -514       -174       -512       -258       -358 


50                                          SUBTRACTION  Oral 

i.    From  15,  25,  35,  45,  55,  65,  75,  85,  95,  take  6,  7, 
8,  and  9. 

2.  Take  7,  8,  and  9  from  each  of  the  following  num- 
bers :  16,  26,  36,  46,  56,  66,  76,  86,  and  96. 

3.  17      27      37      47      57       67       77       87  97 
_8     -8     -8     -8     -8     -8      -8      -8  -8 


4.  17 

27 

37 

47 

57 

67 

77 

87 

97 

-9 

-9 

-9 

-9 

-9 

-9 

-9 

-9 

-9 

5.  18 

28 

38 

48 

58 

68 

78 

88 

98 

-9 

-9 

-9 

-9 

-9 

-9 

-9 

-9 

-9 

6.  Twenty  boys  went  camping.  All  but  9  of  them 
caught  cold.     How  many  boys  caught  cold  ? 

7.  A  mother  hen  hatched  13  chickens.  Only  8  of 
them  lived.     How  many  died  ? 

8.  i I °    If   it 

is  24  miles  from  A  to  C,  and  8  miles  from  A  to  B,  how 
far  is  it  from  B  to  C  f 

9.  Ted  rode  his  bicycle  18  miles  from  home.  He 
turned  about  and  had  ridden  12  miles  toward  home  when 
his  tire  burst,  so  that  he  had  to  walk.  How  far  had  he  to 
walk  ?     (Picture.) 

10.    5  yards  are  how  much  more  than  9  feet  ? 

n.  Anna  bought  a  tablet  for  8  cents.  If  she  gave  the 
clerk  a  quarter  of  a  dollar,  how  much  change  should  she 
receive  ? 


Oral  SUBTRACTION  51 

i.  18-10  =  ?  What  can  you  do  with  10  and  8  to 
get  18  ? 

2.  What  can  you  do  with  12  and  5  to  get  7  ?  With  5 
and  7  to  get  12  ? 

3.  13-?=9     9  +  ?=13     13?9  =  4     9?4  =  13 

4.  Henry  earned  $15.  He  bought  some  clothes  for  $7 
and  put  the  rest  of  his  money  in  the  bank.  How  much 
did  he  put  in  the  bank  ?     How  do  you  find  it  ? 

5.  If  Henry  put  $8  in  the  bank  and  spent  $7  for  clothes, 
how  would  you  find  the  number  of  dollars  he  had  at  first  ? 

6.  12,  18,  6.  Show  all  the  things  that  you  can  do  with 
two  of  these  numbers  to  get  the  other. 

Written 

1.     467         Find   the   remainder.     Add   the   remainder   and 
325      subtrahend.     What  do  you  get  ?     If  you  should  not 

get  the  minuend  when  }^ou  add  the  subtrahend  and 

remainder,  what  would  you  think  was  the  reason  ? 
Since  you  do  get  the  minuend  by  adding  the  subtrahend  and  re- 
mainder, what  does  it  tell  you  about  the  remainder  ?  How  can  you 
find  out  whether  any  remainder  is  correct  ? 

In  the  following  examples,  find  the  remainders  and  test  your  work 
by  adding  the  remainder  and  subtrahend. 

2.   342   3.   987   4.   658   5.   709   6.   917 
-121     -603     -435    -209    -615 

7.  $52.63    a  $82.49    9.  $16.81   10.  $12.81 
-12.91      -26.39      -7.19      -9.35 


52  SUBTRACTION  Written 

Find  the  remainders  and  test  your  work : 
1.    763         2.    307         3.   625         4.    653         5.    719 
528  164  218  435  217 

6.    947         7.   456         a    887         9.   715        10.   984 
615  295  479  263  237 

11.     $9.35       12.      $2.19       13.      $9.10       14.    $17.25 
2.48  1.36  3.50  9.32 

15.    $59.20       is.    $49.37       17.    $81.79       is.    865 
28.30  25.66  15.63  429 

19.    $12.93       20.      $2.06       21.     $4.37       22.    $19.28 
5.09  1.96  .85  15.00 

23.  Mr.  Brown  bought  a  horse  for  $245  and  sold  it  for 
$190.     How  much  did  he  lose  ? 

24.  Clarence  bought  a  sheep  for  $3.75  and  sold  it  for 
$5.80.     How  much  did  he  gain  ? 

25.  Six  hundred  seven  pupils  are  enrolled  in  our  school. 
Five  hundred  ninety-three  are  present.  How  many  are 
absent  ? 

26.  There  are  956  men  in  a  parade ;  784  of  them  are 
on  foot.     How  many  are  riding  ? 

27.  1296        28.      4381         29.      981        30.     7120 
-473  -2073  -973  -500 

31.      2013        32.        408        33.      607        34.       370 
-1005  -231  -583  -219 


Oral  ADDITION   AND   SUBTRACTION  53 

i.    9  and  8  are  the  two  parts  of .     8  is  one  part 

of  17 ;  the  other  part  is . 

2.  One  part  of  25  is  7.     What  is  the  other  ? 

3.  William  earned  $.01  on  Monday,  $.02  on  Tuesday, 
$.03  on  Wednesday,  and  so  on  through  the  week.  How 
much  did  he  earn  ? 

4.  Tom  and  Joe  caught  23  trout.  Joe  caught  12  of 
them.     Tom  caught . 

5.  Jessie  and  her  mother  pared  32  apples.    Jessie  pared 


six.     Her  mother  pared . 

6.  A  postman  had  15  days'  vacation.     He  went  away 
for  8  days.     How  many  days  did  he  stay  at  home  ? 

7.  Ethel  earned  two  dimes  and  2  nickels.     In  all  she 
earned cents. 

Written 
Add  toward  the  top,  then  toward  the  bottom : 


i.  621 

2.  106 

3.  264 

4.  563 

s.  462 

143 

342 

341 

692 

153 

254 

260 

173 

118 

247 

326 

406 

462 

209 

321 

243 

347 

374 

712 

145 

6.  598 

7.  390 

s.  635 

9.  264 

io.  246 

321 

408 

962 

324 

314 

607 

761 

48 

149 

270 

53 

29 

307 

254 

186 

908 

382 

42 

326 

409 

54 


PROBLEMS  IN   TEMPERATURE 


Written 


l  The  degree  of  heat  that  anything  has  is 
called  its  temperature.  What  is  it  that  measures 
temperature  ?  When  the  liquid  in  the  thermom- 
eter rises>  is  it  growing  warmer  or  colder  ?  When 
the  liquid  goes  down  ? 

2.  Find  zero  (0)  on  this  thermometer.  What 
temperature  does  this  thermometer  show  now  ? 

3.  Find  the  freezing  point.  That  is  how  many 
degrees  above  zero?  It  is  how  many  degrees 
below  the  boiling  point? 

4.  When  the  thermometer  out  of  doors  shows 
10  degrees  (10°)  below  zero,  what  do  you  think 
the  season  is  ?  It  is  how  many  degrees  below  the 
freezing  point  ?  What  is  the  season  when  it 
shows  90  degrees  (90°)  above  zero? 

5.  When  it  is  49°  above  zero  at  sunrise  and  18° 
higher  at  noon,  what  is  the  temperature  at  noon  ? 

6.  When  the  city  water  is  at  58°,  how  much 
must  it  be  heated  before  it  boils?  How  many 
degrees  must  it  cool  before  it  freezes  ? 

7.  The  temperature  of  the  body  is  98°  above  0. 
It  is  how  much  above  the  freezing  point  ? 

8.  Look  at  the  schoolroom  thermometer  and 
tell  how  warm  the  room  is.  It  is  how  much 
cooler  than  your  body? 

Note.  —  Many  more  exercises  may  be  given,  using  the 
schoolroom  thermometer  in  various  locations. 


Written  ADDITION  AND  SUBTRACTION  55 

1.  Subtract  and  test  your  work : 

a.      6324         b.      4713  c.    $78.21         d.  $63.92 

4516  2804  34.05  44.08 

2.  Add  two  hundred  nine,  five  hundred  thirty-two, 
thirty-six,  one  thousand  three  hundred  twenty-five,  and 
eight  hundred  ten. 

3.  Add  $564.32,  $34.27,  $248,  $6.03,  and  $48.27. 

4.  A  tank  held  634  gallons  of  oil.  218  gallons  leaked 
out.     How  much  remained  ? 

5.  A  grocer  sold  539  pounds  of  coffee  and  had  756 
pounds  left.     How  many  pounds  had  he  at  first  ? 

6.  $465.32  +  $234.16  4-  $72.18  +  $8  +  $5.01  =  ? 

7.  Separate  506  into  two  parts,  one  part  being  153. 

8.  The  two  parts  of  a  number  are  479  and  1088.  Find 
the  number. 

9.  Claude  has  $5.08  in  the  school  bank,  $16.24  in  the 
city  savings  bank,  and  $1.38  in  his  purse.  How  much 
money  has  he  ? 

10.  A  farmer  sold  a  load  of  potatoes  to  a  grocer  for 
$23.20.  He  bought  some  sugar,  tea,  and  flour  for  $14.18. 
How  much  money  should  he  receive  ? 

n.  A  man  sold  a  harness  for  $12.75,  receiving  for  it  a 
load  of  wood  and  $7.80.     What  was  the  wood  worth  ? 

12.    Find  the  difference  between  : 

a.  589  and  692.  d.   $345.16  and  $192.95. 

b.  437  and  928.  e.   3246  and  8109. 

c.  $52.26  and  $16.19.     /.  235  and  1047. 


56  REVIEW  Oral 

i.  Some  of  the  things  that  we  have  learned  : 

a.  pints  make  a  quart. 

b.  There  are quarts  in  a  gallon. 

c.  inches  make  1  foot. 

d.  One  yard  is  the  same  as feet. 

e.  One  dollar  is  equal  to cents. 

/.  A  half  dime  is cents. 

g.  Ten  cents  make  one . 

h.  The  numbers  added  are . 

i.  The  result  of  addition  is  the . 

j.  The  number  from  which  a  number  is  subtracted  is 

the . 

k.  The  remainder  or  difference  is . 


Z.     We  may  test  our  work  in  subtraction  by 


2.  A  house  that  is  8  yd.  wide  is feet  wide. 

3.  A  cow  that  gives  12  qt.  of  milk  gives gallons. 

4.  A  rule  that  is  24  inches  long  is feet  long. 

5.  Two  dimes  and  a  half  dime  make  cents,  or 

one  of  a  dollar. 

,  6.    Express  your  age  in  Roman  numerals. 

7.  There  are    24   rosebushes  in  3  equal  rows;   how 
many  in  a  row?     (Picture.) 

8.  How  many  oranges  at  4  cents  apiece  can  I  get  for 
2  dimes  ? 

9.  Harold  is  9  years  old.     How  old  will  he  be  8  years 
from  now?     12  years?     16  years?     7  years?     13  years? 

10.   Count  by  8's  to  32  ;  by  fours ;  by  2's. 


Written  REVIEW  57 

i.  A  merchant  bought  459  yd.  of  silk,  847  yd.  of  flan- 
nel, 1027  yd.  of  muslin,  439  yd.  of  prints,  and  2348  yd.  of 
broadcloth.     How  many  yards  did  he  buy  ? 

2.  A  city  has  429  miles  of  streets.  If  238  miles  are 
paved,  how  many  miles  are  unpaved  ?     Test  your  work. 

3.  Add  three  thousand  forty  dollars  fifteen  cents ;  two 
hundred  twenty-seven  dollars  fifty-six  cents ;  and  ten  dol- 
lars forty-nine  cents. 

4.  Two  men  start  from  the  same  place  ;  one  travels  east 
983  miles;  the  other  travels  west  479  miles.  They  are 
then  how  many  miles  apart  ?     (Picture.) 

5.  A  man  earned  $  581  in  one  year,  $  748  the  next, 
and  $857  the  next.  a.  How  much  did  he  earn  in  the 
three  years?  b.  If  he  spent  $1479,  how  much  did  he 
save  ? 

6.  Express  in  Roman  numerals : 

a.  The  number  of  feet  in  a  yard. 

b.  The  number  of  quarts  in  a  gallon. 

c.  The  number  of  feet  in  7  yards. 

d.  The  number  of  inches  in  a  foot. 

e.  The  number  of  cents  in  a  dime. 
/.  The  difference  between  25  and  8. 
g.  The  number  of  cents  in  two  dimes. 
A.  Your  age. 

i.   The  number  of  pints  in  2  gallons. 

j.    The  number  of  school  days  in  3  weeks. 

7.  Write  in  figures  VI,  VIII,  IX,  XI,  XIII,  XIV,  XVIII,. 
XXII,  XIX,  XXIV. 


58  REVIEW  Oral 

i.  Eight  years  from  now  May  will  be  20  years  old. 
How  old  is  she  now  ? 

2.  What  coin  is  J  of  20  cents  ?  |  of  20  cents  ?  \  of 
a  dollar  ? 

3.  Nellie  had  21  cents  and  spent  J-  of  it.  a.  How 
many  cents  did  she  spend  ?  b.  How  many  cents  has  she 
left? 

4.  There  are  24  hours  in  one  day.  How  many  hours 
in  £  of  a  day  ? 

5.  Eight  2's  less  five  3's  are  how  many  ? 

6.  Five  kittens  have  how  many  paws? 

7.  Six  squares  have  how  many  corners?  Cut  them 
from  paper,  then  fold  them  into  halves  and  quarters. 

8.  Kate  had  33  peaches  and  gave  away  9.  How  many 
had  she  then  ? 

9.  If  3  pounds  of  dates  cost  21  cents,  what  will  one 
pound  cost  ?     What  will  2  pounds  cost  ? 

10.    12  +  ?  =  22       ?  +  9  =  21       12  +  11  =  ?      10  +  ?  =  22 
ii.    Read   5007;   2010;    5080;   XIX;   XIV;    XXIII; 
XIII;  IX. 

12.  24  lemons  are  how  many  dozen  ? 

13.  Make  a  problem  for  7  +  6 ;  for  3x6;  for  21  — 11 ; 
for  15-*-3;  for  2x7;  for  12-5-2;  for  10  +  5. 

14.  2  dozen  oranges  less  6  are  how  many  ? 
is.    Add  and  subtract: 

14       35      49       85      76      27      68      53      93 
853753497 


Oral  MULTIPLICATION  AND  DIVISION  59 

i.  How  many  2's  in  10?  18?  20?  12?  14?  24?  22? 

2.  What  is  i  of  8?  4?  10?  16?  12?  14?  24?  20? 

3.  Count  by  3's  to  24  and  back;  from  2  to  26  and  back. 

4.  How  many  3's  in  24,  18,  12,  21,  15,  9,  6? 

5.  What  is  £  of  6?  9?  15?  21?  12?  18?  24? 

6.  4  +  4  +  4  +  4  +  4  =  ?  How  many  4's  did  yon  add  to 
get  20?  Then  20  is  how  many  4's?  In  what  other  way 
than  by  addition  can  you  find  five  fours  ? 

7.  Count  by  3's  until  you  have  the  sum  of  five  3's. 

8.  In  what  other  way  could  you  have  found  the  value 
of  five  3's  ?     Which  is  the  shorter  way  ? 

9.  Find,  by  addition,  seven  4's;  eight  4's;  nine  4's; 
ten  4's ;  eleven  4's ;  twelve  4's. 

io.    How  many  4's  in  40  ?  28?  36?  44?  16? 

ii.   What  is  J  of  24?  12?  16?  44?  36?  28? 

12.  How  many  are   three   4's?     Five   4's?     Ten   4's? 
Twelve  4's?    Nine  4's?    Eleven  4's?    Eighths?    Six  4's? 

13.  20 

16  How  many  4's  are  there  in  20?    How  did 

—  4  we  find  it  ? 

12  In  the  same  way,  find  how  many  3's  there 

-4  are  in  12;  3's  in  27;   4's  in  32;   5's  in  30; 

8  5's  in  40;  4's  in  48;  5's  in  60. 

4 


60 


MULTIPLICATION   AND  DIVISION 


Oral 


28       12  30  6's 

2.  What  is  the  cost  of  twelve  2- cent  stamps? 

3.  Jessie  is  9  years  old ;  her  brother  is  twice  as  old. 
How  old  is  her  brother  ? 

4.  How  many  pints  will  a  10-quart  pail  hold  ? 

5.  How  many  pints  in  a  gallon  ?  In  2  gallons  ?  In 
3  gallons? 

6.  a.  Our  schoolroom  is  36  feet  long.  How  many 
yards  long  is  it  ?  b.  It  is  9  yards  wide.  How  many  feet 
wide  is  it  ? 

7.  Five  gallons  of  oil  will  fill  a  quart  lamp  how  many 
times? 

8.  If  3  lemons  will  make  a  pitcherful  of  lemonade, 
how  many  such  pitchers  of  lemonade  will  a  dozen  lemons 
make? 

9.  Twenty-four  eggs  are  how  many  dozen  ?     48  eggs  ? 
10.     5      10        5        6      12  5        5        4        6 

x2      x5      x4      x5     x5      xll      x3      x6      x5 


Written  MULTIPLICATION  M 

i.   If  one  cow  costs  $  42,  what  will  4  cows  cost  ?    Find 
it  by  addition. 

We  may  also  find  it  by  multiplication,  thus: 

$  42      4  times  2  units  are  8  units. 

4     4  times  4  tens  are  16  tens,  or  1  hundred  and  6  tens. 
diQgg     $  168.     Answer. 

Multiply  and  test  your  work  by  addition  : 
2.  64  3.  82  4.  51  5.  94  6.  93 

J?         A         A         A         A 

7.  71  8.  82  9.  41         10.  83         u.  71 

_5  _3  _6  _2  __6 

12.  843       is.  544       14.  932       is.  510       is.  811 
_2  _2  _2  J>  _5 

17.  802  cents   is.  601  cents   19.  712  cents  20.  433  cents 

A  A  A  A 

21.  510  cents  22.  $8.02         23.  $6.01        24.  $7.12 
_6  4  5  4 

25.  If  John's  coat  cost  $4.20,  what  must  be  paid  for  3 
such  coats  ? 

26.  Find  the  cost  of  5  colts  at  $41  apiece. 

27.  Find  the  cost  of : 

a.  Three  bushels  of  apples  at  63  cents  a  bushel. 

6.  Four  pounds  of  steak  at  22  cents  a  pound. 

c.  Five  baskets  of  peaches  at  $1.10  a  basket. 

d.  Two  city  lots  at  $  940  apiece. 


62 


MULTIPLICATION 


Written 


73     4  times  3  units  are  12  units  =  1  ten  and  2  units. 
a     4  times  7  tens  are  28  tens. 


292 


28  tens  +  1  ten  =  29  tens  =  2  hundreds  and  9  tens. 
292.    Answer. 


2. 


48  Multiplicand. 

2  Multiplier. 
96  Product 


The  number  multiplied  is  the 
multiplicand. 

77ie  number  by  which  we  multi- 
ply is  the  multiplier. 

The  result  of  multiplication  is 
the  product. 

Multiply  and  test  your  work  by  addition : 
3.  69     4.    79     5.    65     6.    78     i.  431     a  243     9.  45 
2  2  3  3  4  3  6 


10. 

82     11. 

531    12.  263 

13. 

984    14.  782    15.  ! 

85    16.  873 

4 

3             3 

2             3 

3             2 

17. 

$2.83 
2 

is.    $4.84 
2 

19. 

$3.82     20.  $6.51 
4                  5 

21.  $5.18 
3 

22. 

$7.19 
3 

23.     $1.62 
4 

24. 

$5.91     25.  $8.09 
5                  4 

26.  $4.15 
6 

27. 

$7.19 

28.  $66.21 

29. 

$2.47     30.    $921 

31.   $450 

3 

4 

2                  4 

3 

32. 

$17.08 
3 

33.  $16.05 
4 

34.  $42.83 
2 

35.  $34.84 
2 

36.  Read: 

a.    The  multiplier  in  example  35.     b.   The  product  in 
example  32.     c.   The  multiplicand  in  example  25. 


Oral  REVIEW  63 

i.   Add  7  to  4,  8,  9,  5,  17,  16,  2,  and  11. 

2.    Subtract  8  from  14,  24,  34,  44,  54,  64,  74,  84,  94. 


3.  24 

34 

44 

54   64 

74 

84 

94   104 

-7 

-7 

—  7  - 

-7  -1 

-7 

-7 

-7   -7 

4.  Subtract  9  from  14,  24,  34, 

44,  54 

,64, 

74,  84,  94. 

5.   21 

42 

73 

56 

32 

71 

54   81 

-7 

-8 

-9 

-8 

-3 

-7 

-6   -7 

6.  33 

71 

83 

96 

73 

52 

42   61 

-4 

-2 

-4 

-9 

-8 

-5 

-3   -9 

7.  4)32     5)25     4)28    4)48    3)21     3)27     3)24     2)24 

8.  3)36     5)45    2)22    4)36    4)40    4)24     4)28     7)28 

Written 

9.  813    10.  493    li.  290    12.  840    13.   237    14.  800 
-633       -234       -164       -650       -156       -720 

15.   931    is.  815    17.  790    is.  841    19.   126    20.  371 
-702       -442       -683        -724         -86       -232 

21.    Find  the  difference  between : 
a.  234  and  986.     6.  642  and  437.     c.  $29.38  and  $46.91. 
d.  834  and  1052.   e.  293  and  86.       /.  6428  and  9275. 


64  ROMAN"  NUMERALS 

i.   XXV  =  20  +  5  =  25.  XXVI  =  20  +  6  =  26. 

XXVIII  =  20  +  8  =  ? 

2.  XXIX  =  20  +  9  =  29.         XXX  =10 +  10 +  10  =  ? 
XXXI  =  31.     XXXII  -  ? 

3.  XXXIII  =  30  +  3  =  33.       XXXIV  =  30  +  4  =  34. 
XXXV  =  ? 

4.  XXXVI  =  30  +  6  =  36.     XXXVII  =  30  +  7  =  ? 
XXXVIII  =  ? 

5.  39  =  30  +  9.     Write  it  in  Roman. 

6.  L  =  50.     LI  =  51.     LIV  =  50  +  4  =  ? 

7.  Write  55  in  Roman.     Write  56,  57,  58,  59. 

8.  XL  =  50  -  10  =  ?     XLI  =  40  +  1  =  ?     XLII  =  ? 

9.  Write  in  Roman  43,  44,  45,  46,  47,  48,  49. 

10.   LX  =  50  + 10  =  ?     LXV  =  ?     Write  66,  68,  69. 

ii.   LXX  =  50  +  20  =  ?     Write  72,  74,  75,  76,  78,  79. 

12.   LXXX  =  50  +  30  =  ?     Write  81,  83,  84,  86,  87,  89. 

is.   C  =  100.     XC  =  100-10  =  90.     XCII  =  90  +  2  =  ? 

14.   Write  93,  94,  95,  96,  97,  98,  99. 

Read  the  following  examples  in  class. 

Copy  them  in  figures  and  find  the  products. 

is.   XXVIII  x  IV        is.   XIX  x  III      17.   XLxV 
is.   LVxIV  19.   LXV  x  III      20.   XLIVxVI 

21.    LXXVIIIxIII       22.    XCVIIxII     23.    XCIVxIV 
24.     LXXXIXxIII        25.    XLIXxII        26.     LIXxV 

27.  A  set  of  books  consists  of  3  volumes.  Each,  volume 
contains  LXXXV  chapters.  How  many  chapters  in  all 
the  volumes  ? 


Written  DIVISION  65 

i.    A  farmer  raised  864  bushels  of  oats  and  sold  half  of 

them.     How  many  bushels  did  he  sell  ? 

432  bushels     ■£  of  8  hundreds  =  4  hundreds. 

n\ool  h     11       i  °f  °*  tens  =  ^  tens* 

■|  of  4  units  =  2  units.    432  bushels.    Answer. 

2.  2)426   3.  2)284   4.  2)648   5.  2)886   6.  3)936 

7.  3)630   8.  4)884   9.  4)408  10.  5)550  11.  6)606 
12.  }  of' 660  =  ?   13.  J  of  933  =  ?   14.  J  of  840  =  ? 

Dividend                Divisor         Quotient 
15.    682  divided  by  2       =    

The  number  divided  is  the  dividend. 

The  number  by  ivhich  ice  divide  is  the  divisor. 

The  result  of  division  is  the  quotient. 

Find  the  quotients : 

Dividend        Divisor  Dividend        Divisor 

is.    480  4  is.    336  3 

17.    606  6  19.     505  5 

20.  A  farmer  brought  248  eggs  to  market.  -J-  of  them 
were  broken.     How  many  eggs  were  broken  ? 

21.  Two  hundred  sixty-six  pupils  attend  a  certain  school. 
There  are  just  as  many  boys  as  girls.  How  many  boys  are 
there  ?     How  many  girls  ? 

cents  cents  cents 

22.  4)448  cents        26.   3)933  cents        30.   2)228  cents 


23.  4)$T48  27.   3)$  9.33  31.   2)$2^8 

24.  8446-2  28.    6060-3  32.    6060-*- 6 

25.  $5.50-*- 5  29.    $6.93-*- 3  33.    $24.88-*- 2 


66 


REVIEW 


Oral 


i.    One  orange  for  5  ^,  a  lemon  for  2  f,  and  a  pineapple 
for  15^  cost  how  much?     (Picture.) 

2.  11  ft.  is  how  much  more  than  3  yd.  ? 

3.  Three  quarts  more  than  4  gal.  are  how  many  quarts  ? 

4.  30  boys  are  arranged  in  5  equal  lines.     How  many 
boys  in  each  line  ?     (Picture.) 

5.  If  1  man  can  build  a  wall  in  27  days,  in  how  many 
days  ought  3  men  to  build  it  ? 

6.  In  4  weeks  there  are  how  many  school  days  ? 

7.  How  many  weeks  in  21  days  ? 

a   40  +  20  =  ?     50  +  30  =  ?     16  +  12  =  ?     57  +  9  =  ? 
9.   \  of  24  cents  are  how  many  cents  ? 

10.  Add  2,  3,  4,  5,  and  6  to  14,  25,  36,  47,  and  58. 

11.  Add  6,  7,  8,  and  9  to  14,  25,  36,  47,  58,  and  69. 

12.  Add  5,  6,  7,  8,  and  9  to  16,  38,  57,  89,  and  65. 

13.  Count  by  6's  from  0  to  72. 

14.  One  pint  more  than  12  qt.  is  how  many  pt.  ? 


Add  each  of  the  numbers 
in  the  outer  ring  to  every 
number  in  the  inner  ring. 


Written  REVIEW  67 

i.   369  +  483  +  754  +  96  +  9  =  ? 

2.  432x2  =  ?     561x2  =  ?     823x3  =  ?    483x3  =  ? 

3.  There  are  144  pencils  in  a  gross.     How  many  are 
there  in  2  gross  ? 

4.  Lucy  divided  486  beads  equally  between  Mabel  and 
Sarah.     How  many  did  Mabel  receive  ?     Sarah  ? 

5.  a.  Some  of  our  expenses  for  a  year  are : 

Food  $462.23     b.  If  our  income  is  $1292.50, 

Clothing  154.35         how  much  have  we  left? 

Doctor  and  Medicine    48.54*  c.  How  much  is  our  income 
Taxes  61.08         for  3  years  ? 

Books  and  Papers        28.40     d.  What  are  these  expenses 
Fuel  and  Light  68.39  for  2  years  ? 

Total 

6.  Albert  has  collected  191  postage  stamps.     Ralph 
has  5  times  as  many.     How  many  has  Ralph  ? 

7.  237  +  ?  =  543.     543-?  =  237.     306  +  ?  =  543. 

8.  How  many  quarts  in  862  gallons  ? 

9.  How  many  quarts  in  862  pints  ? 
10.   How  many  pints  in  232  gallons  ? 

n.    Find  by  addition  twelve  5's ;  seven  4's ;  twelve  3's ; 
four  8's  ;  five  10's  ;  four  ll's ;  eleven  4's. 

12.  Find  by  subtraction  how  many  4's  in  48 ;  7's  in  35; 
5's  in  35  ;  4's  in  32  ;  8's  in  32  ;  ll's  in  44  ;  4's  in  44. 

13.  Write  the  table  of  2's  to  2  x  12. 

14.  Write  the  table  of  3's.      15.   Write  the  table  of  4's. 
16.    Write  the  table  of  5's. 


68  MULTIPLICATION   AND  DIVISION  Oral 

1.  Add  five  6's  ;.  add  six  6's ;  add  seven  6's;  eight  6's; 
nine  6's ;  ten  6's ;  eleven  6's ;  twelve  6's.  Learn  the 
sums,  and  recite  them,  thus :  Six  6's  are ,  etc. 

2.  How  many  6's  in  30  ?  How  many  5's  in  30  ? 
30  +  6=?     30-5=? 

3.  30  =  6x ;         30  =  5x ;         7x6  = ; 

42  +  6  = ;  42  +  7  = . 

4.  How  many  6's  in  42  ?     How  many  7's  in  42  ? 

5.    =6x9;  54  +  6  = ;  54  +  9  = . 

6.  How  many  6's  in  54  ?  *How  many  9's  in  54  ?  -^  of 
54=  ?    £of  54=  ? 

7.  Eight  6's  are ;     6  eights  are  ;     \  of  48 

;   lof  48  = ;    6x =  48;    8x =  48; 


there  are 6's  in  48 ;  there  are 8's  in  48. 

8.  How  many  6's  in  60  ?  How  many  10's  ?  \  of 
60=  ?    TVof  60=  ? 

9.  There  are  6  arithmetics  in  a  package.  How  many 
arithmetics  in  7  such  packages?  In  5,. 6,  8,  10,  9  such 
packages  ? 

10.  If  Arthur  can  walk  6  miles  in  a  day,  in  how  many 
days  can  he  walk  24  miles  ?     36  miles  ?     42  miles  ? 

li.  60  is  how  many  6's?  What  must  we  add  to  60 
to  get  eleven  6's  ?     Twelve  6's  ? 

12.  6x11  = ;        12x6  = ;        72  +  6  = ; 

72  +  12  = ;        l  of    72  = ;        ^  of   66  = ; 

6x =66;  xl2  =  72;   11  x =66. 

13.  Write  the  table  of  6's  through  6  x  12. 


Written  MULTIPLICATION  69 

6  times  8  units  =  48  units  =  4  tens  +  8  units. 
1.  438       6  times  3  tens  =  18  tens. 

6       18  tens  -f  4  tens  =  22  tens  =  2  hundreds  -f  2  tens. 
2528       ^  times  4  hundreds  =  24  hundreds. 

24  hundreds  -f-  2  hundreds  =  26  hundreds  =  2  thousands 
+-  6  hundreds.     2628  Product. 

Find  products  and  test  your  work  by  addition  :  fy\At  VK 

376x6.  is.    $8.90x4.     *£^£J*a 

207  x  6. 

$18.06x6.       ~     smkJ-a 

$15.21x6. 

$14.06x5. 

$.79x4. 

$.93x6. 

$2.18x5. 

26.  Six  rows  of    peach  trees,  58  in  a  row,  are  how 
many  trees? 

27.  219  tons  of  coal  at  $6  a  ton  cost  how  much ? 

28.  Find  4  times  763  by  addition ;  by  multiplication. 

29.  a.  653         h.  462        c.  325        d.  433        6.  529 

3  4  5  4  6 


2. 

341  X  6. 

10. 

3. 

79x6. 

li. 

4. 

88x6. 

12. 

5. 

72x6. 

13. 

6. 

537  x  6. 

14. 

7. 

169  x  6. 

15. 

8. 

635x6. 

16. 

9. 

249  x  6. 

17. 

18. 

$8.90x4. 

19. 

$359.87x6 

20. 

385  x  6. 

21. 

706  x  6. 

22. 

395  x  6. 

23. 

617x6. 

24. 

534x6. 

25. 

729  x  6. 

— — 

~- — 

30.  a.   453 

4 

I.   632 
3 

c.  725 
5 

d.   634 

4 

e.  426 
3 

3i.  a.   405 
6 

b.   327 

4 

e.   309 
3 

d.   630 
6 

6.  743 
5 

32.    How  many  working  days  in  349  weeks  ? 


70  MULTIPLICATION  AND  DIVISION  Oral 

1.  Find  in  two  ways  the  value  of  seven  7's ;  eight  7's  ; 
nine  7's ;  ten  7's. 

2.  7x9  = ;  7x7= ;  7x10= . 

3.  35  is  the  product  of  what  two  numbers  ?  56  ?  63  ? 
70?    42?    49?     28?     21?     14? 

4.  1  of  70  = ;  i  of  49= ;  1  of  63  = ; 

l0f  28  = ;  iof  35= ;  1  of  56= . 

5.  7xll  =  ?     How  did  you  find  it  ?     7x12  =  ? 

6.  8is|ofwhat?    9?    11?    6?     7?     12?     5?     4? 

7.  How  many  7's  are  there  in  21?  35?  49?  70? 
84?    63?    77?    56?    42?    28? 

8.  A  schoolroom  has  7  rows  of  desks  with  8  in  a  row. 
How  many  desks  in  all  ?     (Picture.) 

9.  If  there  were  42  desks  in  6  rows,  how  many  would 
there  be  in  a  row  ?     (Picture.) 

io.    Seven  boys  gathered  49  qt.  of  nuts  and  shared  them 
equally.     How  many  quarts  were  there  for  each  boy  ? 

Written 

1.  Multiply  by  7:  a.  32.  b.  45.  c.  67.  d.  53. 
e.  86.  /  95.  g.  123.  h.  84.  I  $42.90.  /  $13.28. 
k.  .$.99.        I  548  pints.       m.  764  yards.       n.  196  feet. 

2.  Multiply  841 :  a.  by  3 ;  b.  by  4 ;  c.  by  5 ;  d.  by  6. 

3.  Multiply  $29.12:  a.  by  5 ;  b.  by  6 ;  c  by  7. 

4.  Multiply  $4.09:  a.  by  3;    b.  by  4;    c.  by  7. 

5.  How  many  days  in  98  weeks  ? 

6.  If  a  man  earns  $  725  a  year,  how  much  will  he  earn 
in  7  years  ? 


Oral  MULTIPLICATION  AND  DIVISION  71 

i.  The  multiplicand  and  multiplier  are  factors  of  the 
product.  In  7  x  9  =  63,  which  number  is  the  product  ? 
Which  are  factors? 

2.  Name  two  factors  of  21;  28;  15;  42;  63;  56; 
44;  55;  77;  32;  40;  72;  49;  48. 

3.  4x =36;  5x =60;  4x =  44. 

4.  7  is  a  factor  of  35.     What  is  another  factor  ? 

5.  Answer  the  following  without  writing  either  question 
or  answer  : 

42x2        56x2        81x4        92x5        321x2 
421x3        32-S-2        93-3      408-4        609  +  6 

6.  Count  by  8's  from  0  to  96  and  back. 

7.  Find  eight  8's  by  addition.     Name  2  factors  of  64. 

8.  Add  8  to  64.     How  many  8's  in  72  ?     8x?  =  72. 

9.  8x10  =  ?    8xll  =  ?    8x12  =  ?    8x?  =  80. 

io.  8  and  12  are  factors  of  what  number  ?  8  and  10  ? 
8  and  11?     8  and  7  ?     8  and  9  ?     8  and  6  ?     8  and  5? 

li.  When  a  product  and  one  of  its  factors  are  given, 
how  can  you  find  the  other  factor  ? 

12.  9x8  =  ?  9x9  =  ?  9x10  =  ?  9xll  =  ?  9x12  =  ? 

13.  How  many  9's  are  there  in  36  ?  54  ?  45  ?  63  ?  81  ? 

14.  How  many  9's  in  72  ?  108  ?  90  ?  99  ? 

15.  Give  the  multiplication  table  of  9's ;  of  8's ;  of  7's ; 
of  6's;  of  5's;  of  4's;  of  3's;  of  2's. 

16.  Give  the  missing  factor : 

108  =  9x -;  81  =  9x ;  63  =  9x . 


72  MULTIPLICATION 


Jl 


Quart  Peck  Bushel 

Note.  —  These  measures  should  be  before  the  class  and  used  by 
the  pupils.  Sawdust,  oats,  or  any  other  light,  dry  material  may  be 
used  to  advantage. 

1.  Which  measure  is  largest  ? 

2.  Which  is  next  ?      3.    Which  is  the  smallest  ? 

4.  How  many  times  do  you  think  a  bushel  of  oats 
would  fill  the  peck  measure  ?     Try  it  and  see. 

5.  How  many  quarts  do  you  think  would  be  needed 
to  fill  the  peck  measure  ?     Try  it  and  see. 

6.  How  many  quarts  make  a  peck?  How  many 
pecks  make  a  bushel  ? 

7.  Name  some  things  that  are  measured  with  these 
measures. 

8.  bu.  stands  for  bushel,  ph.  for  peck,  and  qt.  for 
quart.  The  dry  quart  is  a  little  larger  than  the  liquid 
quart.  A  half  peck  is  how  many  dry  quarts?  How 
does  it  compare  with  a  gallon? 

9.  Find  the  number  of  quarts  in  a.  53  pk. ;  I.  49  pk. ; 
c.  85  pk. ;  d.  136  pk. ;  e.   841  pk. ;  /.  79  pk. ;  g.  ,257  pk. 

10.  Find  the  number  of  pecks  in  a.  908  bu. ;  b.  568  bu.; 
c.  912  bu.;  d.  846  bu.;  e.  932  bu.;/.  711  bu.;  g.  894 bu. 


Oral 


REVIEW 


73 


i.  Count  by  7's  to  84;  by  8's  to  96  ;  by  9's  to  108. 

2.  What  two  factors  make  36?  44?  55?  48?  64?  72? 

3.  The  product  of  two  numbers  is  84.     One  of  them 
is  7.     What  is  the  other  ? 

4.  A  two-bushel  bag  will  hold  how  many  pecks  ? 

5.  36  pecks  of  apples  will  fill  how  many  bushel  crates  ? 

6.  A  quart  is  what  part  of  a  peck  ? 

7.  What  will  a  peck  of  berries  cost  at  12 $  a  quart? 

8.  Answer  at  sight : 


2)486    3)933 

4}880 

5)105 

6)660 

986   323    249 
-475  +921   +120 

86 

-24 

405 
x_4 

422    622 
x3    x3 

Multiply  every  number  in  Subtract  each  number  in 
the  outer  ring  by  each  num-  the  outer  ring  from  every 
ber  in  the  inner  ring.  number  in  the  inner  ring. 


74 


REVIEW 


Written 


i.    See  how  quickly  you  can  get  these  . 
a.  169        6.980        c.  $4.07        A  691        e.-396pk. 
x6  x7  x8  -384  x8 

2.  a.  If  a  sleeping  car  is  69  ft.  long,  how  long  is  a  train 
of  9  such  cars?  b.  If  the  engine  and  tender  are  57  ftc 
long,  what  is  the  entire  length  of  the  train  ? 

3.  Seven  coal  trains  have  47  cars  in  each  train. 
a.  How  many  cars  in  all  ?  b.  If  each  car  carries  9  tons 
of  ccalj  how  many  tons  are  carried  by  all  the  cars  ? 

4.  Copy  this  diagram.  Wherever  a  column  and  a  line 
cross  each  other,  write  the  product  of  the  numbers  given 
at  the  top  of  the  column  and  at  the  left  of  the  line,  as, 
10x8  =  80;  4x5  =  20. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

1 

2 

3 

4 

5 

20 

6 

7 

8 

9 

10 

80 

11 

12 

Oral  DIVISION  75 

1.  How  many  2's  in  5,  and  how  many  over  ?     In  7  ? 
In  11?     In  19? 

2.  How  many  3's  in  8,  and  how  many  over  ?     In  11  ? 
In  16?     In  14?     In  22  ? 

3.  How  many  4's  in  23,  and  how  many  over  ?     In  33? 
In  15  ?     In  21  ?     In  38  ? 

4.  In  47  there  are 5's  and over.     Recite  in 

the  same  way  about   16;  23;  39;  18;  46;  33;  64;  57. 

5.  Tell  how  many  9's  and  how  many  over  in  11;  46  ; 
87;  39;  43;  86;  98;  53;  69;  76;  49;  108;  32. 

The  number  left  over  when  the  dividend  does  not  exactly 
contain  the  divisor  is  called  the  remainder. 

Dividend     Divisor     Quotient     Remainder 
26      -*•       6      =        4  and         2  over 
Test :  6       x         4   +  2  =  26  Dividend. 

6.  Divide  each  of  the  following  numbers  by  2,  3,  4,  5,  6, 
7,  8,  and  9,  and  test  your  answers  as  above : 

7      12      14      38      23      30      19      13      11      17      28 
34      32      29      15      10        8      24      31      26      39      35 

7.  Divide  each  of  the  following  numbers  by  5,  6?  7,  8, 
and  9,  and  test  your  answers : 

44      40      52      49      55      42      46      50      59      61      41 
51      43      45      53      57      60      48      56      47      54      58 

8.  Divide  each  of  the  following  numbers  by  7,  8,  and  9, 
and  test  your  answers  : 

62      72      75      67      65      70      73      74      66      63      76 
71      68      64      81      79      82      78      80      77      69      83 


76  DIVISION  Written 

1.  64  Quotient  Process 
8)512 

48    tens        5  hundreds  does  not  contain  8  any  hundred 
32  units       times ;  5  hundreds  and  1  ten  make  51  tens;  51 
tens  divided  by  8  equals  6  tens  and  3  tens  over ;  3  tens  and  2  units 
make  32  units.     32  divided  by  8  =  4.     64  Quotient. 

The  figures  and  words  below  the  dividend  may  be  omitted,  and 

64  Quotient         8)512 
the  work  expressed  thus  8)512  or       64  Quotient 

2.  Find  J  of  81;  168;  261;  195;  294;  1488;  1971. 
How    can   you   test   your   work?      The   quotient   and 

divisor  are  what  of  the  dividend? 

3.  Find  the  number  of  gallons  in  236  qt. ;  148  qt. ; 
112  qt. ;  244  qt. ;  216  qt. ;  944  qt.;  2324  qt. 

4.  How  many  school  weeks  in  165  school  days  ?  245 
school  days  ?  445  school  days  ?  625  school  days  ? 

5.  Lucy's  father  worked  348  days.     How  many  weeks 
did  he  work  ? 

6.  a.   4)232    b.   3)311      c.   4]SS2 
d.   5JH3F    e.   5)2iTU   /.   3J720 

Find  the  quotients  and  test  your  work  by  midtiplication. 

7.  £of  39;  45;  51;. 57;  63;  69;  72;  78;  81;  102. 

8.  J  of  56;  64;  72;  76;  84;  92;  104;  112;  120. 

9.  Icf  65;  75;  80;  95;  125;  140;    150;  145;  160. 
10.  \oi  78;  90;  102;  114;  120;  132;  144;  168;  180. 
n.  lof  91;  105;  119;  133;  147;  161;   175;  189. 
12.  \  of  104;  120;  136;  152;  168;  184;  200;  232. 
is.  h  of  486;  298;  754;  9312;  8476;  7352;  3578. 


Oral 


MULTIPLICATION    AND   DIVISION 


77 


1.  Divide  by  3 
36;  24;  15 

2.  Divide  by  4 
36;  24;  16 

3.  Divide  by  5 
20;  25;  45 

4.  Divide  by  6 
48;  24;  55 

5.  Divide  by  7 
21;  14;  84 

6.  Divide  by  8 
32;  48;  80 


;  18;  9;  21;  27;  6;  24;  39;  42. 
40;  20;  32;  8;  44;  48;  28;  52. 
50;  35;  60;  40;  30;  55;  65. 
12;  42;  18;  72;  60;  30;  66;  120. 
70;  56;  35;  77;  28;  42;  49;  98. 
56;  64;  24;  96;  88;  40;  72;  144. 


7.  Divide  by  9 
81;  72;  54;  45;  18;  36;  90;  108;  63;  135. 

8.  A  bushel  of  cranberries  cost  $  2.52.     What  was  the 
cost  of  a  peck  ?     (^  of  252  cents.) 

9.  Give  two  factors  whose  product  is  12;  8;  24;  18; 
21;  36;  42;  84;  108;  72;  81;  56;  63;  54;  42;  32;  16. 

10.  Find   by  addition   and   multiplication :    three   7's ; 
four  8's ;  five  5's ;  three  12's ;  three  ll's ;  six  12's. 

11.  A  table  has  4  sides,  each  4  ft.  long.     How  far  is  it 
around  the  table  ?     (Picture.) 


12. 


Multiply  each  number  in  the  upper  row  by  every  number  in  the 
lower  row. 


2 

3 

5 

8 

7 

10 

6 

9 

4 

12 

1 

11 

11 

6 

2 

10 

3 

1 

4 

7 

12 

9 

5 

8 

78  MULTIPLICATION  AND  DIVISION  Written 

i.  3)552      2.  4)164      3.  6)738      4.  3)222      5.  8)336 


6.  5)400      7.  6)336      a.  5)785      9.  7)287    10.  5)670 
11.  4)816    12.  6)378    13.  7)245    14.  3)267    15.  8)432 

is.  5)575    17.  4)356    is.  5]63o    19.  5)490    20.  6)804 

21.  Four  boys  bought  a  boat  for  $  140.     What  should 
each  pay? 

22.  185  books  were  put  on  5  shelves.     How  many  was 
that  for  each  shelf? 

23.  A  room  has  7  rows  of  chairs  with  19  chairs  in  each 
row.     How  many  chairs  in  the  room  ?     (Picture.) 

24.  Multiply  by  3 : 

28;  65;  47;  124;  253;  769;  483;  204;  910. 

25.  Multiply  by  4 : 

49;  385;  769;  428;  349;  206;  908;  839. 

26.  Multiply  by  5 : 

563;  721;  432;  86;  742;  938;  701;  650. 

27.  Multiply  by  6  : 

432;  591;  763;  284;  315;  91;  38;  409;  840. 

28.  Multiply  by  7  : 

63;  40;  51;  48;  39;  415;  521;  230;  408;  916. 

29.  Multiply  by  8  : 

41;  13;  76;  83;  44;  26;  715;  403;  847;  936. 

30.  Multiply  by  9  : 

17;  21;  42;  35;  40;  56;  123;  235;  368;  987. 

31.  Divide  by  7  and  test  your  work : 

105;  133;  154;  217;  392;  469;  595;  651;  623;  952. 


Oral  REVIEW  79 

i.    Count  to  80  by5's;  6's;  7's;  8's;  9's;  10's;  ll's. 

2.  Four  books  at  $  .08  apiece  cost  how  much  ? 

3.  $.20  for  4  oranges  is  how  much  apiece ? 

4.  A  half  dollar,  2  quarters,  a  dime,  and  2  nickels  are 
how  much  money  ? 

5.  a.  How  much  will  I  have  left  out  of    $  32  after 
buying  a  coat  for  $11  ?     b.  64  quarts  =  how  many  pecks  ? 

6.  4  dolls  at  $  .15  apiece  cost  how  much  ? 

7.  28  eggs  sold  out  of  4  dozen  leave  how  many  ? 

8.  3  dimes  will  buy  how  many  bananas  at  3 1  apiece  ? 

9.  Bananas  at  $  .48  a  dozen  are  how  much  apiece  ? 

10.  From  a  rope  24  ft.  long,  Joe  cut  8  ft.  for  a  jumping 
rope  and  7  ft.  for  hammock  ropes.  How  many  feet  were 
cut ,  off  ?  How  many  feet  were  left  ?  How  many  inches 
long  was  the  jumping  rope  ?     The  piece  that  was  left  ? 

li.  If  mother  needs  2  dozen  buttons  for  Grace's  dress 
and  has  17  buttons,  how  many  must  she  buy  ? 

Written 

1.  a.  Subtract  723  from  1213.     h.  Subtract  24  from  £ 
of  96. 

2.  Add  $4.20,  $3.24,  $2.16,  $.21,  and  $2.43. 

3.  One  factor  of  168  is  6.     What  is  the  other? 

4.  29  and  5  are  the  factors  of  what  number  ? 

5.  See  hoiu  quickly  you  can  get  the  answers  to  these : 
a.  232  +  467  +  229.        c.  $36.45        d.  672        e.  4]3B 
6.  306  4-184-200.  -14.29  -280        /.  5]M5 


80  MULTIPLICATION   AND   DIVISION  Written 

1.  Multiply  each  of  these  numbers  by  7,  8,  9,  and,  10: 

a.  37;  36;  31;  35;  34;  33;  32;  38;  39. 

b.  63;  65;  64;  62;  67;  68;  61;  69;  66. 

c.  84;  82;  85;  89;  86;  83;  81;  88;  87;  80. 

d.  93;  94;  95;  96;  92;  97;  99;  98;  91. 

2.  Find  |  of  104;  120;  136;  152;  168;  184;  200. 

3.  Find  1  of  117;  135;  153;  171;  189;  207;  225. 
Find  quotients  and  remainders.     Test  your  work. 

4.  DicidebyS:  41;  43;  46;  49;  53;  56;  79;  94. 

5.  Divide  by  4:  53;  58;  62;  70;  74;  98;  106;  138. 

6.  Divide  by  5:   78;  83;  94;  102;  112;  118;  123. 

7.  Divide  by  6:  81;  88;  93;  99;  165;  110;  136. 

8.  Divide  by  7:  95;  99;  107;  115;   120;  129;  145. 

9.  Divide  by  8:  108;  115;  124;  138;  147;  165. 
io.    Divide  ly  9:  121;  128;  138;  156;  167;  187. 

n.   Lewis's  hens  laid  154  eggs  in  a  week.     That  was 
how  many  eggs  a  day  ? 

12.  Copy  in  figures  and  find  the  product :  LXVIII  x  IX. 

13.  Find  the  cost  of  9  carriages  at  $  257  apiece. 

14.  At  how  much  apiece  must  8  cows  be  sold  to  bring 
$368? 

15.  Copy  in  figures  and  find  the  quotient :  XCVI  -s-  IV. 

16.  How  many  weeks  in  161  days ;  245  days ;  448  days  ; 
623  days ;  497  days ;  945  days  ? 

17.  8)232     9)441     7)651     5)335     5)2410"    9)1107 

18.  426  is :  a.  \  of  what  number  ?     b.  ^  of  what  ? 


Oral  REVIEW  81 

i.    8  +  3  +  2  +  5  +  7  +  6-8=  ?       4  +  8  +  9-6  +  10=? 

2.  Lewis  bought  a  pencil  for  3  cents  and  a  writing  pad 
for  8  cents.  How  much  change  should  he  get  from  a 
quarter  ? 

3.  In  a  flock  of  57  sheep  9  died.     How  many  lived  ? 

4.  Give  two  factors  which  make  81 ;  64 ;  49 ;  36 ;  56 ; 
63;  72;  96;  84;  48;  77;  99;  144. 

5.  One  factor  of  121  is  11.     What  is  the  other? 

6.  Write  in  Roman  the  numbers  of  the  chapters  in  a 
book  from  Chapter  XXXVIII  to  Chapter  LX. 

7.  Two  peaches  at  2^  apiece  and  5  oranges  at  3^  apiece 
cost  how  much  ? 

8.  a.  3  +  9  +  5-4-2  +  9=  ?  6.4x9-3=? 
c.  6x8-12=  ? 

9.  How  many  months  in  11  years  ? 

10.    Make  a  problem  for  8  x  7  ;  for  6x5;  for  4x12. 
li.    9  x  12  =  - .     Make  a  problem. 

12.  A  half-peck  of  chestnuts  at  5^  a  quart  cost  how 
much  ? 

13.  12  bu.  of  oats  will  feed  how  many  horses  if  each 
horse  eats  a  peck  ? 

14.  a.  1  gal.  =  pt. ;  h.  1  yd.=  in.;  c.  1  bu. 

= qt. 

15.  If  we  sing  7  exercises  every  day,  how  many  shall 
we  sing  in  a  week  ? 

16.  The  sum  of  two  numbers  is  24.     One  of  them  is  6. 
What  is  the  other  ? 


82  REVIEW  Written 


i.    Add. 

Write 

sums 

only. 

Do  not  copy  the  addends. 

Can  you  get 

correct 

sums 

:  in  3  minutes  ? 

a.  749        b 

83 

.  476 
584 

c. 

754 
326 

d. 

$  128.04 
36.12 

e.  1271 
564 

365 

693 

473 

17.49 

329 

872 

227 

538 

216.20 

613 

574 

456 

842 

538.52 

706 

633 

843 

695 

6.37 

473 

497 

709 

972 

49.59 

856 

2.  From  8293  take 

a.   467;  b.   548;  c.  2439;  d.  7584;  e.  3965;/.  684. 

3.  a.    714  b.   1264  c.  207  d.   273  e.  807  /.  561 

x8     x7    x9    x9    x8    x7 

4.  a.   7]3l7     b.  8)268     c.  9)288     d.  6)2454     e.  5)170 

5.  a.   5)6700    6.  4)196    c.  7)658    d.  9)T683    e.  8)1184 

6.  Three  ranchmen  own  3978  sheep.  If  their  shares 
are  alike,  how  many  sheep  does  each  man  own  ? 

7.  A  peddler's  sales  for  a  week  are:  Monday,  $6.18; 
Tuesday,  $4.23;  Wednesday,  $7;  Thursday,  $16.85; 
Friday,  $3.98;  Saturday,  $27.39.  a.  Find  the  total  for 
the  week.  b.  At  the  same  rate,  what  would  be  the  total 
for  9  weeks  ?     c.  For  7  weeks  ?     d.  For  8  weeks  ? 

8.  Mr.  Jones  raised  583  bu.  of  corn,  which  was  276  bu. 
more  than  Mr.  Brown  raised.  How  many  bushels  did 
Mr.  Brown  raise  ? 


TIME 


83 


l.    Which  is  the  hour  hand? 

Which  is  the  minute  hand  ? 

What  is  the  other  hand? 

To  what  number  does  the  hour 
hand  point?     The  minute  hand? 

How  many  hour  spaces  are 
there  on  the  dial?  How  many 
hours  is  it  from  noon  to  mid- 
night? From  midnight  to  noon?  How  many  hours  in 
a  whole  day? 

2.  How  long  does  it  take  the  minute  hand  to  go  around 
the  dial  ?  How  many  minute  spaces  between  XII  and  I  ? 
Between  X  and  XI  ?  How  many  minute  spaces  on  the 
whole  dial  ?     How  many  minutes  make  an  hour  ? 

3.  How  many  times  will  the  minute  hand  pass  around 
the  dial  between  12  o'clock  and  1  o'clock  ?  Between  12 
and  4  ?     Between  2  and  5  ?    Between  4  and  9  ? 

How  many  minutes  are  there  in  2  hours  ?     In  7  hours  ? 

4.  The  second  hand  passes  around  the  circle  once  every 
minute.     How  many  seconds  make  a  minute  ? 

5.  What  time  is  shown  on  the  dial  ? 

6.  When  the  minute  hand  reaches  VI,  where  will  the 
hour  hand  be  ?  What  time  will  it  be  ?  When  the  minute 
hand  reaches  I,  what  time  will  it  be?  When  it  reaches 
II;  III;  nil;  V;  VI;  VII;  VIII;  IX;  X;  XI;  XII? 

7.  When  the  hour  hand  is  after  V  and  the  minute  hand 
is  at  III,  what  is  the  time  ?     (Picture.) 


84  TIME 

Summary 

seconds  (sec.)  make  1 

minutes  (min.)  make  1 

hours  (hr.)  make  1 (da.) 

BEADING  AND  WKITING  NUMBERS 

| 

JLJL 

467,507  is  read  four  hundred  sixty-seven  thousand  five 
hundred  seven. 

10,450  is  read  ten  thousand  four  hundred  fifty. 

-    l.   Read : 

512,239  42,000  639,010 

759,283  354,000  420,216 

569,351  20,514  25,004 

306,429  1,006  106,000 

26,381  150,213  70,016 

10,450  40,208  236,700 

2.  Write  :     a.  One  thousand  five  hundred  seventy-four. 

6.  Two  hundred  thirty-four  thousand   six 
hundred  ninety-seven. 

c.  Fifty-nine  thousand. 

d.  Sixty  thousand  four  hundred  thirty. 

3.  Make  a  watch  dial  showing  half-past  ten. 

4.  Write  in  Eoman  the  number  of  hours  in  a  day; 
seconds  in  a  minute  ;  hours  in  half  a*  day  ;  minutes  in  half 
an  hour ;  minutes  in  a  quarter  of  an  hour ;  hours  in  two 
days ;  hours  from  5  in  the  morning  to  7  at  night. 


ORAL   PRACTICE 

85 

i.    20  +  10 

2.     40  +  20 

3. 

20  +  70 

4.    40  +  50 

30  +  10 

40  +  30 

20  +  80 

60  +  40 

20  +  20 

50  +  20 

20  +  90 

70  +  40 

30  +  30 

60  +  20 

50  +  30 

50  +  80 

30  +  20 

70  +  10 

30  +  60 

90  +  60 

5.    70-20 

6.    80-40 

7. 

60-40 

8.    50-30 

90-10 

90-30 

70-50 

70  -  60 

50-20 

70-10 

30-20 

90-40 

30-10 

60-20 

80-50 

70-40 

60-30 

90-80 

90-60 

80-20 

9.    10x8 

10.    30x4 

11. 

50x7 

12.      6  x  20 

20x2 

50x3 

60x8 

3x80 

60x3 

70x3 

30x6 

5x90 

40x5 

60x2 

40x9 

2x60 

70x2 

90x4 

80x2 

7x30 

is.   25  +  10 

14.    16  +  40 

15. 

39  +  10 

16.    76  +  20 

45  +  20 

27  +  30 

84  +  10 

24  +  50 

35  +  30 

58  +  20 

21  +  30 

19  +  80 

65  +  10 

85  +  10 

35  +  20 

72  +  20 

35  +  20 

17  +  40 

42  +  30 

61  +  30 

it.   26-10 

is.    73-50 

19. 

89-50 

20.    83-50 

42-10 

84-20 

72-40 

79-20 

83-20 

96-30 

99-70 

92-80 

56-30 

88-50 

83-40 

61-30 

27-10 

79-60 

64-50 

82-60 

7x90 

8x40 

6x70 

2x80 

86  PRACTICE  IN  ADDITION  AND  SUBTRACTION         Oral 

1.   Add  2,  3,  4,  5,  6,  7,  8,  9  to  each  of  the  following 
numbers : 


a. 

b. 

c. 

d. 

e. 

/• 

g- 

h. 

i. 

57 

19 

55 

72 

74 

58 

26 

77 

82 

44 

69 

98 

42 

35 

68 

37 

56 

53 

52 

74 

75 

83 

54 

38 

49 

89 

62 

64 

15 

66 

46 

17 

36 

28 

48 

96 

85 

105 

63 

88 

87 

73 

16 

92 

93 

59 

18 

47 

76 

39 

45 

67 

78 

27 

86 

29 

99 

84 

65 

95 

79 

25 

97 

2.  Subtract  2,  3,  4,  5,  6,  7,  8,  9  from  each  of  the  above 
numbers. 

3.  Pupils  by  turn  add  columns  aloud,  one  pupil  writing 
the  sums  on  the  blackboard. 

65  +  27  =  ?        Say  65,  85,  92. 

4.  i  65  +  20  =  85. 

85+   7  =  92.  An*. 
In  the  same  way  give  the  sums  of  the  following  : 

5.  24  +  25.      9.    37  +  58.    is.    64  +  27.     17.    63  +  29. 


6. 

38  +  43. 

10. 

23  +  34. 

14. 

81  +  19. 

18. 

34  +  38. 

7. 

72  +  19. 

11. 

58  +  45. 

IS. 

59  +  21. 

19. 

33  +  68. 

8.  1 

35  +  16. 

12. 

43  +  59. 

16. 

58  +  34. 

20. 

92  +  19. 

65-27< 

=  ? 

Say  65, 

45, 

38. 

21. 

65-20 

45-  7 

=  45 
=  38 

Ana. 

22.  ' 

72-19. 

25. 

76-29. 

28. 

82-44. 

31. 

45-18. 

23.  ! 

35-16. 

26. 

93  -  37. 

29. 

91-23. 

32. 

37-19. 

24.  1 

S3 -25. 

27. 

64-35. 

30, 

78-31. 

33. 

92-78. 

Written  SUBTRACTION-  87 

l.    Mr.  Emerson  bought  a  stock  of  groceries  for  $  3897 
and  sold  them  for  $  5296.      How   much  did  he  gain  ? 

_        .  After  we  have  taken  1  ten  from  9  tens  in  the  minuend, 

^  how  many  tens  are  left  ?     We  cannot  take  the  9  tens 

g  iQnrt  A        in  the  subtrahend  from  the  8  tens  left  in  the  minuend, 
so  what  must  we  do  ? 

Test  all  your  work.   The  subtrahend  +  the  remainder  =  ? 

2.    842    3.     435    4.     583    5.     694    6.     803    7.     715 

647  238  245  598  654  678 

a    5643       9.    4521      10.    3462      u.     3573 
2738  2618  2548  1628 

la.    6411      13.     5343      14.    4701      is.    3603 
2508  2517  2654  1672 

16.    5007      17.    3541      is.    4504      19.    4791 
2548  2496  1576  2432 

20.  $421.35    21.  $846.30    22.  $6937.15    23.  $2341.17 
143.29  298.41  486.29  1935.48 

24.     1200    25.   1000  26.  $439.21  27.     8435  28.     4605 
1199  983  248.41  6598  2719 

29.  How  much  money  must  be  added  to  $  436  to  make 
$1321? 

30.  In  the  year  1895  Mr.  Finch  had  $  4378  in  the  bank. 
In  1903  he  had  $  5247.  a.  How  much  did  he  save  in 
that  time  ?    b.   In  how  many  years  did  he  save  it  ? 


88  REVIEW  Written 

Can  you  get  the  first  five  right  in  tivo  minutes  f     Write 


only  tlie  answers. 

1.   403 

2.    $12.50 

516 

1.35 

940 

6.23 

768 

1.79 

24 

7.00 

3. 

419 
-263 

6. 

708 
x7 

4. 

576 

x9 

7. 

375 

x9 

2)8642 


,    467 
x6 

9.    Mr.  West  is  6  ft.  tall.     How  many  inches  tall  is  he  ? 

10.  A  window  sill  is  84  inches  from  the  ground.  How 
many  feet  above  the  ground  is  it  ? 

li.  A  merchant  bought  goods  amounting  to  $  530  and 
paid  $  260  down.     How  much  did  he  still  owe? 

12.  If  a  steamboat  goes  512  miles  in  a  day,  how  far 
will  it  go  in  6  days  ? 

13.  $42.10      14.    $39.24      is.    $18.19       ie.    $4.93 

x6  x5  x4  x3 

17.  The  subtrahend  is  $  375.39,  the  minuend  $  483.29. 
Find  the  remainder. 

is.  1476  is  the  difference  between  4325  and  what  other 
number  ? 

is.  5462  20.  2000  21.  4605  22.  $30.06  23.  2741 
-2735  -729       -2719  -12.74         -659 

24.  A  train  of  9  cars  has  79  passengers  in  each  car. 
How  many  passengers  in  all  the  cars  ? 

25.  An  ocean  steamer  can  carry  789  passengers  at  each 
trip.     How  many  can  she  carry  at  7  trips  ? 


MULTIPLICATION  89 

The  value  of  any  figure  depends  on  its  place ;  and  every 
time  a  figure  is  moved  one  place  to  the  left  its  value  is 
multiplied  by  ten,  thus: 

60  =  6  tens=6xl0  =6x10 

600  m  6  hundreds  =6x10x10  =  6  x  100 

6000  =  6  thousands  =  6  x  10  x  10  x  10  =  6  x  1000 

1.  5x10  =  ?  5x100  =  ?  5x1000  =  ? 

2.  9x10  =  ?  9x100  =  ?  9x1000  =  ? 

3.  When  we  multiplied  6,  5,  and    9    by  10,  we   an- 
nexed what  to  them  ?     By  100  ?     By  1000  ? 

4.  How  can  we  multiply  a  number  by  10  ?     By  100  ? 
By  1000? 

5.  Multiply  by  10  : 

7;  43;  55;  79;  3;  436;  581;  3245;  4823. 

6.  Multiply  by  100  : 

8;  9;  7;  4;  3;  2;  14;  81;  37;  40;  324;  561. 

7.  Multiply  by  1000  : 

1;  2;  5;  8;  12;  61;  19;  83;   10;  425;  306;  420. 

8.  If  one  horse  is  worth  $  225,  what  are  30  such  horses" 
worth  ?     How  shall  we  find  it  ? 

*225 

Qfk         30  =  3  X  10 ;  therefore,  multiplying  by  30  is  the  same  as 
multiplying  by  3  and  then  by  10. 


$6750 

9.   Multiply  248  by  30  ;  50  ;  60  ;  80 ;  70  ;  90 ;  40 

10.  29 

700  29  X  700  =  29  X  7  X  100. 

20300 

11.  Multiply  34  by  700 ;  500 ;   200  ;  9000 ;  8000. 


90  MULTIPLICATION  Written 

l.  Mr.  Johnson  sells  threshing  machines  at  $  537 
apiece.  How  much  does  he  receive  for  39  machines  ? 
What  must  we  do  to  find  it? 

537  39  =  30  +  9 ;  therefore,  we  may  multiply  537 

39  by  30  and  by  9  and  add  the  products. 

4833  =  537  X  9  4833  and  16110  are  called  partial  products. 

1611    =  537  x  30  The  0  may  be  omitted  from  units'  place  in  the 


20943  =  537  x  39    second  partial  product 

2.  127      3.  206      4.  346      s.  710 
34            25            15             32 

6.  532 
21 

7.  712 

33 

s.  543      9.  673     10.  274     u.  148 
22            13            16             14 

12.  714 
25 

13.  324 

34 

14.  212  is.  742  is.  632  17.  427  is.  654  19.  475 
16     24     70     63     37     38 

20.  749  21.  746  22.  807  23.  237  2*.  415  25.  474 

67     78     89     78     69     68 

26.  7  sacks  of  flour  at  $1.35  cost  how  much  ? 

27.  6  pounds  of  coffee  for  $1.32  is  how  much  a  pound  ? 

28.  At  $  1.75  a  day,  how  much  can  a  man  earn  in  a 
week  ? 

29.  $  7.35  paid  on  a  debt  of  $  10.00  leaves  how  much 
unpaid  ? 

30.  How  many  chapters  from  chapter  XXVIII  to  chap- 
ter XCIV? 

31.  From  120  apples,  take  7  dozen  apples. 


REVIEW  91 

Quick  Test 

Teacher  dictates  questions.     Pupils  write  answers.     Pass  papers, 
mark  them,  and  make  report. 

1.  How  many  months  are  there  in  11  years  ? 

2.  J  of  a  day  is  how  many  hours  ? 

3.  On  what  number  is  the  minute  hand  at  20  minutes 
past  two  ? 

4.  How  many  seconds  are  there  in  £  of  a  minute  ? 

5.  At  20  f  a  gallon,  what  will  1  qt.  of  milk  cost  ? 

6.  Bought  10  qt.  of  cherries  at  9  ^  a  quart  and  gave 
the  clerk  a  silver  dollar.     What  change  should  I  receive  ? 

7.  Potatoes  at  48  ^  a  bushel  are  how  much  a  peck  ? 

8.  Hickory  nuts  at  5  ^  a  quart  are  how  much  a  peck  ? 

9.  How  many  pints  in  11  gallons  ? 

10.  How  many  days  in  12  weeks  ? 

Oral 

1.  From  100  subtract  30 ;  20 ;  50 ;  80 ;  10 ;  70 ;  40. 

2.  65-28  =  ?    (Say  65,  45,  37.) 

3.  84-28       s.    93-54       i.    59-29        9.    83-26 

4.  76-37       6.   46-38       8.    81-17      10.    48-29 

11.  49x10  = ;   73x100  = ;  8x1000  = . 

12.  How  many  dresses  will  36  yd.  of  silk  make  if  9  yd. 
will  make  one  dress  ? 

13.  3  dozen  eggs  cost  $.39.     One  dozen  costs . 

14.  How  many  minutes  in  8  hours  ?     In  7  hours  ? 


92  MISCELLANEOUS 

Numbers  of  Days  in  the  Different  Months : 

January  31         April  30       July  31  October  31 

February  28       May  31        August  31  November  30 

March  31  June  30       September  30       December  31 

February  has  29  days  once  in  four  years  (Leap  year). 

1.  a.  How  many  days  in  a  common  year  ? 
&.  How  many  days  in  a  leap  year  ? 

c.  Hew  many  June  days  have  you  seen?     July  days? 

d.  How  many  December  days  have  you  seen  ?  April 
days  ? 

e.  How  many  days  in  57  common  years  ? 

/.  How  many  days  in  89  leap  years  ?     44  leap  years  ? 
g.  How  many  hours  are  there  in  a  common  year  ? 
h.  How  many  hours  are  there  in  a  leap  year  ? 
L   How  many  hours  are  there  in  9  leap  years  ? 

2.  How  many  seconds  are  there  in  an  hour? 

3.  How  many  minutes  are  there  in  a  day  ? 

4.  How  many  seconds  are  there  in  a  day  ? 

5.  How  many  school  weeks  in  475  school  days  ? 

6.  If  there  are  8  grades  between  the  kindergarten  and 
the  high  school,  and  it  takes  200  days  to  pass  each  grade, 
how  many  days  must  you  attend  school  to  go  through  all 
the  grades  ? 

7.  Find  the  cost  of  5  books  at  $  1.87  each. 

8.  $203  paid  for  7  cows  is  how  much  apiece  ? 

9.  $152  will  buy  how  many  washing  machines  at 
$  8  each  ? 


FINDING   ANY   PART   OF   A  NUMBER 


I        cent 


r7^ 

cent        I 


I        cent        I 


cent 


of  6  cents  = 
cents. 


1.  Here  are  how  many  cents  ?     -J 
cents,     -§  of  6  cents  =  2  x cents  = 

2.  Make  12  cents.     Find  \  of  12^;  §  of  12*. 

3.  Draw  a  line  20  in.  long. 


Find  J  of  20  in. ;  £  of  20 


in. ;  |  of  20  in. ;  £  of  20  in. ;  f  of  20  in. ;  £  of  20  in. 
4.    Draw  a  line  1  yd.  long.     Mark  the  inches.     J  yd.  is 

inches ;  £  yd.  = in. ;  £•  yd.  = in. 

\  of  a  yard  is inches  ;  -|  yd.  = in. 


are 


^  of  a  yard  is inches ;  |-  yd.  = in. 

Picture  10  marbles.     Mark  off  £  of  10  marbles ;  f. 

|-  of  10  marbles  are marbles ;  f  of  10  marbles 

—  marbles ;  ^  of  10  marbles  are marbles. 


9.  Take  21  splints,  beans,  or  marbles.  Find  ^>  f>  f? 
f ,  f,  f  of  them. 

io.    How  many  eggs  in  f  of  a  dozen  ?     £  of  a  dozen  ? 

li.  A  pie  is  worth  20  cents.  What  is  \  of  it  worth  ? 
|?  |?  i?  s?  4?  Make  two  pictures  of  the  pie.  Cut 
one  into  fourths,  the  other  into  fifths. 

12.  How  many  hours  in  f  of  a  day  ?     f  ?  f-  ?  |  ?  f  ?  £  ? 

13.  If  you  are  awake  J-  of  the  time,  you  are  awake  how 
many  hours  each  day  ?     How  many  hours  do  you  sleep  ? 


94  MISCELLANEOUS  Written 

1      Find  1233425567     5     2     5     7     8nf  0^90 

2.  a.  If  an  acre  of  land  costs  $175,  what  would  84 
acres  cost  ?     b.  J-  of  an  acre  ? 

3.  Mr.  Rich  earns  $25.76  per  week.  His  son  earns  f 
as  much.  a.  How  much  does  the  son  earn  ?  b.  How 
much  more  does  the  father  earn  than  the  son  ?  c.  How 
much  do  both  earn  ? 

4.  Multiply  twenty-nine  thousand  four  hundred  sixty- 
three  by  fifty-seven.     Write  the  product  in  words. 

5.  A  man  had  196  books.  He  gave  his  son  f-  of  them. 
a.  How  many  books  did  the  son  receive  ?  b.  How  many 
did  the  man  keep  ? 

6.  The  Revolutionary  War  began  in  1775,  and  the 
Spanish  War  in  1898.  How  many  years  between  the 
two  wars  ? 

7.  a.  Find  the  product  of  842  and  76.     b.  27684-^9  =  ? 

8.  Bought  a  carriage  for  $125  and  sold  it  for  $98. 
How  much  did  I  lose  ? 

9.  a.  448-7  =  ?  5.390-5  =  ?  c.  863x9  =  ? 
10.    A  man  having   320  sheep  sold  284.     How  many 

had  he  left? 

li.    A  boy  had  saved  $2  and  then  spent  $.60  for  pres- 
ents.    How  much  had  he  left  ? 

12.  Leo  had  $3.68  and  his  father  gave  him  enough  to 
make  $5.00.     How  much  did  his  father  give  him? 

13.  A  man  owed  $265  and  paid   $199.     How   much 
did  he  still  owe? 


QUICK  TEST  95 

i.  5  +  8  +  7  +  6  +  9  =  ? 

2.  Write  19  in  Roman. 

3.  Find  the  cost  of  8  pounds  of  sugar  at  5  cents  a  pound. 

4.  Add  62  and  31. 

5.  Subtract  49  from  83. 

6.  Find  f  of  28. 

7.  How  many  quarts  in  3  pk.  of  onions? 

8.  120  minutes  are  how  many  hours? 

9.  How  many  inches  in  9  feet  ? 
10.  7x9  +  8-7  =  ? 

Oral  Problems 

1.  If  7  oranges  cost  21  cents,  1  orange  costs cents. 

5  oranges  cost cents.     Make  the  question. 

2.  a.  When  Bessie  picked  5  qt.  of  berries  on  Monday, 
8  on  Tuesday,  and  7  on  Wednesday,  in  the  three  days  she 
picked  quarts. 

b.  If  she  sold  10  quarts  and  gave  the  rest  to  her  mother, 

she  gave  her  mother quarts. 

3'.  If  a  dozen  oranges  cost  48  cents,  1  orange  costs 
cents.     11  oranges  cost  cents.     Question. 

4.  In  10  quarts  there  are pints.      If  1  pt.  of  milk 

costs  3  cents,  20  pints  will  cost cents.     Question. 

5.  If  eggs  are  $.24  a  dozen,  1  egg  costs  cents. 

7  eggs  cost cents.      Question. 

6.  If  10  eggs  cost  30  cents,  1  egg  costs  cents. 

A  dozen  eggs  cost cents.     Question. 


96  PROBLEMS  Oral 

Answer  to  yourself  these  questions  about  each  problem  : 
a.  What  is  asked?  b.  What  is  told?  c.  What  must  1 
find  first  ? 

1.  A  lady  bought  3  dozen  buttons  at*8  cents  a  dozen, 
and  a  yard  of  ribbon  at  10  cents.  What  did  she  pay  for 
both? 

2.  John  walked  4  miles  and  Eoy  walked  five  times  as 
far.     How  far  did  Roy  walk  ?     How  far  did  both  walk  ? 

3.  A  man  earned  $8  one  week,  $  9  the  next,  $10  the 
next.  How  much  money  did  he  earn  in  the  three  weeks  ? 
He  put  $20  in  the  bank  and  spent  the  rest.  How  much 
did  he  spend? 

4.  At  6^  a  quart,  what  will  3  gal.  of  oil  cost? 

5.  How  many  5-cent  car  fares  can  be  paid  with  a  quar- 
ter, a  dime,  and  a  half  dime  ? 

6.  Elsie  bought  a  tablet  for  8  cents,  a  stamp  for  2  cents, 
and  some  pencils  for  9  cents.  She  gave  the  clerk  a  quar- 
ter.    How  much  change  should  she  receive  ? 

7.  A  man  earned  $42  and  used  f  of  it.  How  much 
did  he  use  ?     How  much  had  he  left  ? 

8.  Four  oranges  cost  12  cents.  At  the  same  price, 
what  must  be  paid  for  8  oranges? 

9.  A  man  earns  $  15  a  week  and  saves  \  of  it.  How 
much  does  he  save  in  one  week  ?  How  long  will  it  take 
him  to  save  $  27  ?  How  much  will  he  save  in  12  weeks  ? 
How  much  does  he  spend  in  a  week  ?     In  4  weeks  ? 

10.    Ned  has  three  rabbits  and  Ted  four  times  as  many. 
How  many  has  Ted  ?     How  many  have  both  ? 


Oral 


REVIEW 


97 


1.  A  milkman  had  2  cans  of  milk  with  6  gallons  in 
each  can.     How  many  quarts  of  milk  had  he  ? 

2.  If  5  pencils  cost  15  cents,  what  will  1  pencil  cost? 
What  will  3  pencils  cost?     10  pencils?     11  pencils? 

3.  f  of  a  yard  of  ribbon  is  how  many  inches  long  ? 

4.  A  four-foot  rule  could  be  cut  into  how  many  sticks, 
each  six  inches  long  ? 

5.  3  min.  = sec.     2  hr.  = min. 


4  wk.  =  - 
ihr.=  - 
9  qt.  and  1  pt.  = 

4  doz.  +  3  = 

6  doz. +  11= 


da.      5  yr.  = 


mo. 


min, 


7  gal.  and  3  qt. 
-pt. 

8  doz.  +  2  =  — 
11  doz.  +  6  =  - 


qt. 


39? 

10. 

11. 


How  many  dozen,  and  how  many  over,  in  17  ?    27  ? 
46?     54? 

Multiplication  table,  page  73. 
Read  each  number  in  the  inner 
square   before  every  sign  in  the  outer 
squares,  and  find  the  result 

12.    4x8  +  ?  =  35.     7x9  +  ?=69. 
is.    7x7  +  ?=  58.     8x6  +  ?  =  54. 
14.    What  is  the  time  when  the  hour  hand  is  at  VIII  ? 
Where  is  the  minute  hand  then  ? 

is.  What  is  the  time  when  the  hour  hand  is  between 
V  and  VI  and  the  minute  hand  is  at  III  ?  When  the 
minute  hand  gets  to  IX  ? 

16.    What  is  the  cost  of  2  bu.  of  potatoes  at  10^  a  peck  ? 


+5 

-f2 

-7 

+18 

-t-3 

36 

72 
108 

xio 

-r-6 

-29 

-^9 

-7-4 

-11 

4-9 

98  MISCELLANEOUS  Written 

1.  Find  7  times  389  by  addition  and  by  multiplication. 

2.  Find  by  subtraction  how  many  16's  in  176;  in  96; 
in  144;  in  80;  in  160;  in  112;  in  128. 

3.  Copy  answers  only.    Add  up  and  down.    How  long 
will  it  take  t 


a.   463 

b.  453  c 

•.  $478.45 

d. 

$165.35 

e.   $  4.10 

274 

224 

85.46 

48.64 

467.20 

632 

35 

300.18 

8.03 

254.18 

49 

368 

63.24 

6.00 

325.16 

548 

74 

.65 

17.40 

49.21 

231 

989 

49.85 

5.84 

8.00 

598 

6785 

237.46 

97.68 

77.56 

4.  a.  3642  x  24;  b.  4832  x  34;  c.  2356  x  43;  d.  805  x  96. 

5.  At  our  festival  we  used  125  gallons  of  ice  cream. 

a.  How  many  quarts  were  used  ?     b.  If  each  quart  was 
served  to  6  persons,  how  many  persons  ate  of  the  cream  ? 

6.  a.  A  market  man  bought  1057  pounds  of  beef,  538 
pounds  of  mutton,  and  457  pounds  of  veal.  How  many 
pounds  of  meat  did  he  purchase  ?  b.  After  he  had  sold 
986  pounds  of  meat,  how  many  pounds  remained  ? 

7.  Find    the    quotient    and    remainder :      a.  347  h-  5  ; 

b.  643  +  6;    c.  487  +  8;    d.  3067   <-  9;    e.  4234  -*-  7; 
/.  613  +  9 ;  g.  4134  -*-  8. 

8.  48  bushels  of  potatoes  at  $.55  a  bushel  cost  how 
much  ? 

9.  A  grocer  has  432  bu.  of  potatoes.  How  many 
customers  can  he  supply  with  a  peck  apiece  ? 


Written 

MISCELLANEOUS 

9 

Papers 

sold  by  seven  hoys  during  one  week  : 

Mon.       Tues.       Wed.      Thur. 

Fri. 

Sat 

Henry 

,     .     .     36         28         24         14 

26 

32 

Carl    . 

.    .    .    24        35        25        16 

18 

26 

Jerry  . 

.     .     18        23         26        24 

28 

29 

Frank      , 

.     .     29         18        21         32 

27 

35 

Charles    , 

.    .     15        26        18        27 

34 

36 

Roy     .     , 

,     .     .    34        31        30        28 

26 

27 

Edward 

,     .     .     12         23         20        19 

27 

28 

1.  Find  the  number  of  papers  sold  on  Monday ;  Tues- 
day; Wednesday;  Thursday;  Friday;  Saturday. 

2.  Find  the  number  sold  by  Henry;  Carl;  Jerry; 
Frank ;  Charles ;  Roy ;  Edward. 

3.  Find  :  a.  The  number  sold  on  all  the  days.  b.  The 
number  sold  by  all  the  boys.  c.  How  do  these  two  num- 
bers compare  ? 

4.  a.  714    b.  1264    c.  207    d.  740    e.  1273    /.  6701 

x8  x7         x9  x6  x4  x5 


5.  a.  9)3T7        b.  8)2657        c.  9)2890        d.  9)3069 

6.  At  3^  each,  how  many  lemons  will  72^  buy  ? 

7.  $  6.28  out  of  a  $  10  bill  leaves  how  much  change  ? 

8.  There  are  27  daisies  in  one  vase  and  3  times  as 
many  in  another.     How  many  in  both  vases  ? 

9.  Find  the  cost  of  7  tons  of  coal  at  $4.75  a  ton. 

10.    John  earned  $18  during  the  vacation  and  spent 
%  12.75.     How  much  did  he  save  ? 


100  MULTIPLICATION   AND  DIVISION  Oral 

1.  Moving  a  figure  to  the  left  one  place  multiplies  its 
value  by  10.  Moving  a  figure  one  place  to  the  right  does 
what  to  its  value  ? 

2.  9x10  =  90.   90-10  =  ?  23x10  =  230.  230-10  =  ? 

3.  To  multiply  a  number  by  10  we  annex  a  0. 
How  can  we  divide  a  number  by  10  ? 

4.  Divide  by  10  : 

80;  60;  130;  740;  800;  4360;  560;  1300;  2080. 

5.  To  multiply  a  number  by  100  we  annex  two  ciphers. 
How  can  we  divide  a  number  by  100  if  it  has  ciphers 

at  the  end  ? 

6.  Divide  by  100  : 

600;  900;  1200;  2300;  6000;  48000;  64500;  360000. 

Written 

32 

7.  8P)25W.  80  =  8  x  10,  To  divide  by  80  we  divide 
by  10  and  then  by  8.     How  do  we  divide  by  10  ? 

8.  a.  30)34920     b.  40)2480     c.  50)4750     d.  60)720 

9.  Divide  by  90  : 

a.  1620;  b.  4770;  c.  71100;  d.  108000;  e.  17280. 

iOo    500  =  5  x  100.     How  may  we  divide  4500  by  500  ? 

n.   a.  500)1500  b.  500)7500  c.  700)11200  d.  600)72000 

12    a.  342x60  is.  a.      490-70  14.  a.    4800-80 

b.    34  x  90  b.  34600  -  40            b.  62500  -  500 

c     81  x  700  c.  27900  -*  90             c.  91000  -*-  700 

d.  495  x  310  d.     6420  -  60            d.  34000  -  2000 


Written  REVIEW  101 

i.    Add  up,  then  down.    Write  only  the  sums.    5  minutes  f 
a.  $548.42      b.  4835      e.  4782      d.  63854      e.  $381.15 


57.54 

724 

95 

9763 

42.81 

6.00 

89 

398 

427 

68.73 

.84 

38984 

27579 

5106 

59.42 

346.99 

35 

49895 

78243 

486.53 

24.63 

672 

6879 

4675 

79.49 

51.06 

4897 

4623 

1016 

83.26 

2.  Find  the  differences  and  test  results : 

a.  7821      b.  $200.14      c.  $800.00      d.  7421      e.  8402 
6459  89.27  256.13  1695  1673 

3.  Multiply:  a.  763  by  42.  b,  529  by  44.  e.  862  by  31. 
d.  720  by  43. 

4.  Find :  a.  |  of  2982.  b.  •§-  of  2832.  c.  1  of  5715. 
d.  i  of  2732. 

5.  a.  If  our  living  expenses  are  $7.56  a  week,  how 
much  are  they  for  1  day?  b.  For  9  days?  c.  For  5  days? 
d.  For  4  weeks  ? 

6.  Fiud :  a.  i  of  651.  b.  f  of  651.  c.  £  of  5640. 
d.  i  of  5640. 

7.  a.  43x500.  b.  691x70.  c.  39x3000. 

d.  865x80.  e.  196x39. 

8.  How  many  days  in  the  first  six  months  of  the  year  ? 

9.  Counting  30  days  for  a  month,  how  many  months 
in  180  days? 

10.    How  many  quarts  in  798  bushels  ? 


102  MULTIPLICATION  Written 

i.  If  a  grain  car  will  carry  756  bu.  of  corn,  how 
many  bushels  will  243  such  cars  carry  ?  What  operation 
must  be  performed  ? 

756 

92T8  — 7^6     3  What  is  the  answer?     What 

OAni       ^ra     Af\  have  we  omitted  from  the  second 

3024   =756x40  .  ,        9 

i  en  o      -  Y^fi     900         a      ™*ird  partial  products  f 

183708  =  756x243 

2.  Henry's  kite  string  is  648  ft.  long.  How  many 
feet  of  twine  would  it  take  to  make  207  such  kite  strings  ? 
How  many  partial  products  will  you  have  ?  Where  will 
you  write  the  first  figure  of  the  second  partial  product  ? 

3.  A  tract  of  land  is  laid  out  in  248  lots,  each  one 
for  sale  at  $375.  If  the  owner  sells  all  of  them  at  that 
price,  how  much  will  he  receive  for  them  ? 

4.  Multiply  239  by  158.  Multiply  158  by  239.  How 
do  the  products  compare  ? 

5.  Find  how  412  times  653  compares  with  653  times 
412. 

Find  the  products  in  two  ways  : 


6. 

385x209 

10. 

209  x  506 

14. 

854  x  305 

7. 

842  x  351 

ii. 

983  x  786 

15. 

907x635 

8. 

496  x  258 

12. 

428  x  732 

16. 

294  x  687 

9. 

324  x  807 

13. 

356  x  271 

17. 

839  x  594 

18.    If  a  baggage  car  goes  248  miles  every  day,  how 
many  miles  will  it  go  in  a  year  ? 


AVOIRDUPOIS  WEIGHT  103 

Note.  —  Have  scales  before  the  class. 
i.    For  what  are  the  scales  used  ? 

2.  Find  the  pound  weight. 

3.  Let  each  pupil  take  the  pound 
weight  in  his  hand. 

4.  Name  articles  that  weigh  about  a  pound.  Weigh 
them. 

5.  Put  sand  in  a  bag  until  you  think  you  have  a 
pound.      Weigh  and  correct  it. 

6.  Use  the  bag  of  sand  for  a  pound  weight.  Find  the 
ounce  weight.  Weigh  out  several  ounces  of  sand  in  bags. 
Find  how  many  ounce  bags  are  needed  to  balance  the 
pound  bag. 

7.  There  are ounces  (oz.)  in  1  pound  (lb.). 

8.  Name  articles  that  are  sold  by  the  pound ;  by  the 
ounce. 

9.  How  many  ounces  are  there  in  2  lb.?   3  lb.?   5  lb.? 

10.  How  many  ounces  in  i  lb. ;  J  lb. ;  |-  lb.  ? 

11.  How  many  ounces  in  1J  lb. ;  2J  lb. ;  1J  lb.  ? 

12.  Mr.  Jolly,  the  candy  maker,  gave  away  25  lb.  of 
candy,  putting  1  oz.  into  each  bag.  How  many  bags  of 
candy  did  he  give  away  ? 

13.  a.  How  many  days  will  7  lb.  of  sugar  last  you  if 
you  eat  an  ounce  every  day  ?     h.  How  many  weeks  ? 

14.  If  the  average  weight  of  the  plums  on  a  certain  tree 
is  1  oz.,  how  many  plums  will  it  take  to  weigh  395  lb.  ? 
476  1b.?    |  lb.?    fib.?    |  lb.? 


104  REVIEW  Oral 

i.    How  much  is  |  of  a  peck?     ^  of  $  150? 

2.  If  I  give  a  dollar  in  payment  for  9  qt.  of  peaches  at 
10^  a  quart,  what  change  should  I  receive  ? 

3.  Find  the  sums  and  differences  : 

68      54      78      49       51      63      58      41      53 
2926       16       27       33       37292439 

4.  How  many  feet  in  108  inches?     How  many  yards? 

5.  How  many  times  can  a  two-quart  measure  be  filled 
from  a  bushel  of  walnuts  ? 

6.  I  have  12  rows  of  strawberry  plants  with  12  plants 
in  each  row.     How  many  plants  have  I  ? 

7.  Find  the  cost  of  8  tons  of  rye  straw  at  $  20  a  ton. 

Written 

1.  At  Mann's  store  85  crates  of  Georgia  peaches,  each 
crate  containing  6  baskets,  were  sold  in  1  day. 

a.  How  many  baskets  were  sold  ?     b.   If  there  were  34 
peaches  in  each  basket,  how  many  peaches  were  sold  ? 

2.  a.    If  a  boy  can  ride  his  bicycle  6  miles  an  hour, 
how  many  hours  will  it  take  him  to  ride  288  miles  ? 

b.  If  he  rides  6  hours  a  day,  how  many  days  will  it  take  ? 

3.  From  the  sum  of  4623  and  5498  subtract  their  dif- 
ference. 

4.  If  3  horses  cost  $  678,  what  will  12  horses  cost  at 
the  same  rate  ?     (12  is  how  many  times  3  ?) 

s.      43        6.    231        7.    435        8.    9)649    9.    6)435 
x280  x    600      x309 


Written  DIVISION  105 

l.    A  dealer  bought  13  carriages  for   $  3055.     What 
did  each  cost? 

235 
13)3055  Process 

26  ^  of  30  hundreds  is  2  hundreds  and  4  hundreds  over. 

45     4  hundreds  and  5  tens  are  45  tens.     ^  of  45  tens  is  3  tens 
§9     and  6  tens  over.     6  tens  and  5  units  are  05  units,    ^  of 
65  65  units  is  5  units. 
85 

Find  the  quotients  and  test  your  work  by  multiplication : 


2.  13)2015  9.  13)1599  is.  14)6818  23.  15)3765 

3.  13)2327  10.  13)234  17.  14)5026  24.  15)4575 

4.  13)5993  11.  13JT742  is.  14JT344  25.  15)6420 

5.  13)2769  12.  14)T890  19.  14)7322  26.  15)1845 

6.  13)42l2  13.  14)3430  20.  14)364  27.  15)3l95 

7.  13)975  14.  14)6342  21.  14)3234  28.  16)688 

8.  13)5577  15.  14)3556  22.  15)2025  29.  16)1984 

30.  One  factor  of  247  is  13.  What  is  the  other  factor  ? 

31.  The  product  of  two  numbers  is  6804.     One  of  the 
numbers  is  14.     What  is  the  other  number? 

32.  In  one  mile  there  are  5280  ft.      ^  of  a  mile  =  ?  ft. 

33.  Find  ^  of  364  ;  ^  of  5005  ;  Ji  of  1638 ;  f  of  3556. 

34.  ^  of  1190  =  ?  T\  of  3332  =  ?  if  of  6314  =  ? 

35.  Findf  of  2730;  |;  f;   &;  &;  &J  &J  &. 

36.  How  many  pounds  in  48  oz.  ?    832  oz.  ?    144  oz.  ? 


106  MULTIPLICATION  AND  DIVISION  Written 

-   i.    How  many  quart  boxes  can  be  filled  from  25  bu.  of 
peaches  ? 

2.  ^  bu.  =  qt.     How  many  half-bushel  baskets 

could  be  filled  from  288  qt.  of  chestnuts  ? 

3.  A  four-gallon  can  holds qt.     How  many  four- 
gallon  cans  could  be  filled  from  272  qt.  of  oil  ? 

4.  If  William  earns  $  16  a  month,  how  many  months 
must  he  work  to  earn  $  576  ? 

5.  See  how  quickly  you  can  get  correct  answers : 

a.  3421  x  45 ;  ft.  4326  x  51 ;  c.  5678  x  55 ;  d.  9834  x  43. 

6.  Find  quotients  and  remainders  and  test  your  work : 

a.   5)393;   6.6)497;    c.  7)899;    d.  8)943;  e.  9)4875. 

7.  How  many  pounds  in  2112  oz.  ? 

8.  42  lb.  and  12  oz.  are  how  many  ounces  ? 

9.  At  $  .06  a  quart  what  will  65  gal.  of  milk  cost? 
io.    One  factor  of  675  is  15.     What  is  the  other? 
u.    In  3600  seconds  how  many  minutes  ? 

12.    Find  quotients  and  remainders  and  test  your  work  : 
a.   439  +  13;    ft.   513  +  14;    c.   1835  +  8;    d.   459  +  7. 
is.    Find :  a.  {  of  675 ;   ft.  |  of  732 ;  c.  £  of  580. 
14.    Multiply:  a.  472  by  69;  ft.  803  by  105. 
is.    Divide:  a.  8320  by  20;  ft.  7960  by  40. 

16.  Find  the  number  of  hours  in  the  month  of  October. 

17.  Find  the  number  of  minutes  in  the  month  of  October. 

18.  If  a  man  works  9  hours  a  day,  in  how  many  days 
will  he  work  3681  hr.  ? 


QUICK   TEST  107 

1.  How  many  ounces  in  a  half  pound  ? 

2.  How  many  ounces  in  J  of  a  pound  ? 

3.  How  many  12's  in  52  and  how  many  over  ? 

4.  12  gal.  and  3  qt.  are  how  many  quarts  ? 

5.  At  5  f  a  foot,  what  will  a  yard  of  picture  moulding 
cost? 

6.  A  half  hour  is  how  manj  minutes  ? 

7.  If  you  buy  a  book  for    $.15,   how   much   change 
should  you  get  from  a  quarter  ? 

8.  Four  dimes  and  a  half  dime  are  how  many  cents  ? 

9.  How  many  inches  in  a  yard  ? 

10.   Two  quarts  of  berries  at  10  ^  a  quart  and  a  loaf  of 
bread  at  5^  cost  how  much  ? 

Oral 

1.  How  many  pints  in  4  gal.? 

2.  A  quart  is  what  part  of  a  gallon  ?     2  qt.?     3  qt.? 

3.  f  of  a  yard  is  how  many  inches  ? 

4.  Charles  was  punctual  at  school  every  morning  for 
20  weeks.     How  many  times  was  he  punctual  ? 

5.  |  of  40  =  ?     J  of  40  =  ?     What  part  of  40  is  5  ? 

6.  How  many  6's  in   12  ?     6   is   what   part   of   12? 
6  months  is  what  part  of  a  year  ? 

7.  Sarah's  brother  earns  $  16  a  week  and  saves  \  of  it. 
In  how  many  weeks  can  he  save  %  20  ? 

8.  Candy   at   2  /  an   ounce  is  how  much  a  pound  ? 
What  is  a  quarter  of  a  pound  worth  ?     A  half   pound  ? 


108  REVIEW  Written 

1.  In  48  pecks  there  are  how  many  quarts  ? 

2.  The  Pilgrims  came  to  America  in  1620.  How 
long  ago  was  that? 

3.  Bought  a  lot  for  $  598.  For  what  must  I  sell  it  to 
gain  $59? 

4.  A  milkman  sells  36  gallons  of  milk  every  day. 
a.  How  many  pounds  does  it  weigh  if  a  pint  weighs  a 
pound  ?     b.  How  many  ounces  does  it  weigh  ? 

5.  Robert  bought  some  clothes  for  $5.45.  He  gave 
the  clerk  a  $5  bill  and  a  silver  dollar.  How  much 
change  should  he  receive  ? 

6.  5  tons  of  coal  cost  $27.50.     Find  the  cost  of  1  ton. 

7.  423       s.    524       9.    4031      10.    4706      11.    5072 
-297         -349         -1234  -927  -3095 

12.  Write  in  words:  31,605;  270,040;  341,005;  104,500. 

13.  Write  in  figures :  three  hundred  thousand  twenty  ; 
eighteen  thousand  fourteen ;  six  thousand  three  hundred 
thirty ;  one  hundred  fifty-seven  thousand  nine. 

I*,    a.  f  of  1032;  b.  |  of  992;  c.  f  of  560;  d.  f  of  1675. 

15.  •  From  seventy  dollars  and  twenty-nine  cents  take 
fifty-two  dollars  and  sixty-nine  cents. 

16.  At  30  cents  a  peck,  what  will  3  bu.  of  apples  cost  ? 

17.  A  lady  had  $135.  She  paid  $45  for  a  sewing 
machine  and  $  22  for  cloth.     How  much  has  she  left  ? 

is.  There  are  7  dozen  lemons  in  one  box  and  83  lemons 
in  another.     How  many  lemons  in  both  boxes  ? 


Written  DIVISION   AND  MULTIPLICATION  109 

i.    Divide  1134  by  21.     To  find  the  first  figure  in  the 
quotient,  ask  yourself,  "  How  many  2's  in  11  ?  " 

2.  Divide  by  21: 

a.  8883;        b.  6515;       c.  19677;        d.  9639. 

3.  Divide  2573  by  31.     To  get  the  first  quotient  fig- 
ure say,  "  How  many  3's  in  25? " 

4.  Divide  by  SI: 

a.   2635;   b.   2883;   c.   3875;    d.   14353. 

In  examples  5-19,  find  the  quotients  and  test  your  work 
by  multiplication : 

5.  1599  +  41         10.    814  +  22  15.    2108-62 

6.  6068-41         11.    2912-32         is.    6912-72 

7.  2346  +  51        12.    768-32  17.    4756  +  82 

8.  2275  +  91        13.    3486  +  42        is.    1288  +  92 

9.  1386  +  22         14.    4992  +  52        .19.    2511  +  93 
Find  the  products  and  test  your  work  by  division: 

20.  46x31  22.    124x32  24.    93x52 

21.  53x21  23.    63x61  25.    242x71 

26.  One  factor  of  3844  is  62.     Find  the  other  factor. 

27.  43x?  =  5203.  2a  11070  +  ?  =  82.   29.  ?  x  61  =  1159. 

30.  The  multiplier  is  42.     The  product  is  3444.     What 
can  you  find  ? 

31.  The  divisor  is  78,  the  quotient  467.    What  can  you 
find? 

32.  Lucien  sold  806  papers  in  the  month  of  May.    That 
was  how  many  per  day  ? 


110  MAKING  QUESTIONS 

Every  problem  tells  us  something  and  asks  us  to  find 
something.  We  use  what  is  told,  to  find  what  is  asked. 
The  following  exercises  tell  you  something.  Ask  the 
question  in  each  one  and  answer  it. 

1.    Berries  are  10  cents  a  quart.     John  bought  7  qt. 
2     Mary  had  21  cents.     Oranges  cost  3  cents  apiece. 

3.  Seven  pounds  of  maple  sugar  cost  84  cents. 

4.  Chester  is  5  ft.  tall.    There  are  — —  inches  in  a  foot. 

5.  There  are seconds  in  a  minute.    It  takes  Leah 

5  seconds  to  answer  a  question. 

6.  Chocolate  creams  cost  3  ^  an  ounce.     There   are 
ounces  in  a  pound. 

7.  Frances  earned  11  cents  on  Friday,  9  cents  on  Tues- 
day, and  10  cents  on  Wednesday. 

8.  Richard  earned  41  cents  and  paid  5  ^  for  car  fare. 

9.  Nina  took  a  music  lesson  twice  a  month  for  a  whole 
year.     There  are months  in  a  year. 

10.    Robert  is  14  years  old.     His  sister  Dorothy  is  ten. 
li.    Mary  is  19  years  old.    Frederick  is  7  years  younger. 

12.  Lemons  are  24  cents  a  dozen.  Ethel  bought  6 
lemons. 

13.  There  are  8  hours  in  a  working  day.  Philip  worked 
72  hours. 

14.  Make  a  problem  for  $  .05  +  $  .06  +  $  .07. 

15.  J  of  16  =  ?     Make  a  problem. 

16.  f  of  36  =  ?     Make  a  problem. 

17.  10x2  =  ?     Make  a  problem. 


Oral 


KEVIEW 


111 


i.    John    paid    $.36   for    9   packages   of   flower  seed. 
Question. 

2.  Wilbert  has  a  strip  of  oak  5  ft.  long.     He  is  making 
6-inch  rules.     Question. 

3.  Make  a  problem  for  4  times  12  in. 

4.  A  bushel  of  potatoes  is  worth.  60  cents.     A  peck 
is  of  a  bushel.     Question. 

5.  Alice  made  a  dozen  pop-corn  balls.     Lena  made  three 
times  as  many.     How  many  did  both  make  ? 


3 

6 

2 

12 

11 

4 

10 

8 

5 

9 

7 

x  7,  8,  9. 

7.  At  $  .06  a  pound,  find  the  cost  of  3  lb.  of  starch ; 
81b.;  10  1b.;  9  1b.;  12  1b.;  50  1b.;   111b.;   20  1b.;  7  1b. 

8.  33  bananas  were  sold  from  a  bunch  containing 
7  dozen.     How  many  were  left? 

Written 

1.  January,  March,  May,  July,  August,  October,  and 
December  have  each  31  days.  How  many  days  in  all 
these  months?     Find  it  in  two  ways. 

2.  A  man  in  Vermont  made  388  qt.  of  maple  sirup. 
He  put  it  into  gallon  cans.     Question.      Answer  ? 

3.  Make  a  problem  for  $  84.50  -  $  13.27. 

4.  Make  a  problem  for  38  x  7  da. 

5.  Write  in  words :  304,091;  20,040;  100,001;  $50.03. 

6.  I  saw  an  ocean  steamship  499  feet  long.  There  are 
inches  in  a  foot.     Question.      Answer  ? 


112 


KECTANGLES 


Fig.  1. 


Fig.  2. 


1.  What  is  the  shape  of  Figure  1  ?  How  long  is  it  ? 
How  wide  ? 

What  is  it  called  ?     Describe  a  square  inch  (sq.  in.). 

2.  Without  a  rule,  draw  a  square  inch.  Measure  and 
correct  it. 

3.  The  corners  of  a  square  are  right  angles.  This  is  a 
right  angle  I —     How  many  right  angles  has  a  square  ? 

4.  What  kind  of  angles  has  Figure  2  ? 

5.  How  many  right  angles  has  Figure  1  ?     Figure  2  ? 

6.  Figure  1  and  Figure  2  are  rectangles.  Describe  a 
rectangle. 

7.  A  rectangle  may  be  either  square  or  oblong.  Make 
an  oblong  rectangle  3  in.  long  and  1  in.  wide.  Draw 
lines  catting  it  into  square  inches.  How  many  square 
inches  are  there  ? 

8.  Find  out  how  many  square  inches  in  an  oblong  1  inch 
wide  and  3  inches  long ;  4,  5,  6,  10,  11,  13  inches  long. 

9.  Draw  a  rectangle  three  inches  long  and  2  inches 
wide.     Mark  it  off  into  square  inches  and  count  them. 

10.    Draw  a  square  3  in.  long.     Mark  it  off  into  square 
inches  and  count  them. 


RECTANGLES 


113 


_j , 1 

i ] ! 


1.  What  is  the  name  of  this  figure  ?  How  wide  is  it  ? 
How  long  ?     Its  size  is  3  in.  by  4  in. 

2.  The  dotted  lines  drawn  from  left  to  right  divide  the 
rectangle  into  oblongs  how  long  and  how  wide  ?  How 
many  of  them  ? 

3.  Each  oblong  4  in.  long  and  1  in.  wide  contains  how 
many  square  inches  ?  How  many  square  inches  in  all  of 
them  ?    Three  times  4  sq.  in.  are  how  many  square  inches? 

4.  The  dotted  lines  from  top  to  bottom  divide  the  rec- 
tangle into  how  many  oblongs  ?  Each  of  these  oblongs 
is  how  long  ?  How  wide  ?  It  contains  how  many  square 
inches  ?     All  of  them  contain  how  many  square  inches  ? 


114  MULTIPLICATION  AND  DIVISION  Written 

1.  Draw  a  rectangle  which  you  think  is  6  in.  by  5  in. 
Measure  and  correct  it.  Mark  out  a  row  of  square  inches 
along  one  side  of  it.  How  many  square  inches  in  this 
row?  How  many  such  rows  could  you  make  from  the 
whole  rectangle  ?  How  many  square  inches  in  the  rec- 
tangle ?     5  times  6  sq.  in.  =  ? 

2.  Make  a  rectangle  7  in.  by  4  in.  Mark  it  off  into 
square  inches.  How  many  square  inches  in  the  rectangle  ? 
How  do  you  find  it  ? 

3.  Make  a  rectangle  8  in.  by  6  in.  How  many  square 
inches  does  it  contain  ?     How  do  you  find  it  ? 

4.  On  the  blackboard,  draw  a  rectangle  18  in.  by  7  in. 
How  many  square  inches  does  it  contain  ? 

5.  How  many  square  inches  in  an  oblong  24  in.  by 
12  in.  ?     Make  the  drawing. 

6.  Find  the  number  of  square  inches  in  the  top  of  a 
table  which  is  22  in.  by  38  in. 

Find  the  number  of  square  inches  in  each  of  the  following 
rectangles : 


7. 

39  in.  by  42  in. 

12. 

62  in.  by  37  in, 

8. 

68  in.  by  29  in. 

13. 

41  in.  by  48  in, 

9. 

47  in.  by  33  in. 

14. 

36  in.  by  19  in, 

10. 

59  in.  by  28  in. 

15. 

38  in.  by  40  in, 

11. 

39  in.  by  2  feet. 

16. 

3  ft.  by  20  in. 

17.  a.  A  blackboard  2  ft.  6  in.  wide  is  how  many  inches 
wide  ?  b.  A  blackboard  4  ft.  long  is  how  many  inches 
long  ?  c.  How  many  square  inches  in  a  blackboard  4  ft. 
by  2  ft.  6  in.  ? 


Written  DIVISION  115 

1.  Mr.  Wilson  bought  a  farm  for  $  9044.     How  much 

must  he  save  each  year  to  pay  for  it  in  19  years  ? 
476 

19)$  9044  19   ig   almost   20.     Think  how  many  2's  in  9. 

(20)      76  To  get  the  next  quotient  figure,  think  how  many 

144  2's  in  14.     To  get  the  next  quotient  figure,  think 

233  how  many  2's  in  11.     5  is  a  little  too  small,  because 

11  a  it  gives  a  remainder  19,  the  same  as  the  divisor. 

What  is  the  correct  figure  ? 
114 

2.  Divide  12499  by  29.     (29  is  almost  30.     Let  3  be 
your  guide  figure  and  think  how  many  3's  in  12,  etc.) 

3.  Divide  2808  by  39.     (39  is  almost  40.     What  will 
you  take  for  a  guide  figure?) 

4539-89         is.   14732-58 
2772-99         19.     4420-68 
792-18         20.     6318  +  78 
10584-28         21.   45056-88 
10353-29         22.     6174  +  98 
2242  +  38         23.     3315  +  39 
8064  +  48 
ng  cars  is  522  ft.  long.     How 
long  is  each  car? 

25.  How  many  coal  cars  31  ft.  long  would  make  a  train 
1395  ft.  long? 

26.  When  you  have  a  product  and  one  of  its  factors, 
how  do  you  find  the  other  factor  ?  What  is  the  length  of 
a  rectangle  12  in.  wide  that  contains  840  sq.  in.? 


4. 

2808  +  39 

11. 

5. 

24708  +  29 

12. 

6. 

11837-*- 19 

13. 

7. 

4508  +  49 

14. 

8. 

36639  +  59 

15. 

9. 

16008  +  69 

16. 

10. 

64148  +  79 

17. 

24. 

A  train  of  9 

sleer 

116 


MAKING  CHANGE 


Oral 


In  paying  the  amounts  given  below,  how  much  change 
should  you  receive  from  $  1  ? 

To  find  the  change  for  64  cents,  — 


64+    6 

=  70. 

Think 

70  +  30 

=  100 

. 

Say  6,  36. 

t30  +   6 

=  36 

Am. 

$.12 

$.14 

$.16     $.18 

$.13 

$.15 

$.17 

$.19     $.11 

.25 

.27 

.29       .25 

.21 

.22 

.24 

.26       .28 

.31 

.33 

.35       .37 

.39 

.32 

.34 

.36       .38 

.48 

.46 

.44       .42 

.41 

.43 

.45 

.47       .49 

.56 

.58 

.52       .->  1 

.59 

.57 

.55 

.53       .51 

.61 

.69 

.67      .65 

.63 

.64 

.64 

.66       .62 

.76 

.78 

.77      .72 

.73 

.71 

.75 

.74       .79 

.81 

.88 

.83      .87 

.84 

.85 

.86 

.82       .89 

.95 

.96 

.99       .97 

.94 

.93 

.98 

.91       .92 

Add  the  ( 

jolumns.     Add  the  lines. 

Add  the  sums  of 

the  columns. 

Add  the  sums  of  the  lines.     Compare. 

ROMAN  NUMERALS 

i.  C  =  100.      CC  =  100 +  100  =  200.      CCC  =  100  +  100 
+  100  =  ? 

2.  D  =  500.    CD  =500 -100  =  400.    DC  =  500 +  100  =  ? 

3.  M  =  1000.    CM  =  1000 -100  =  ?    DCCC  =  ? 

4.  C  =  ?    XXVI  =  ?    CXXVI  =  ?    DC  =  ?    LXV  =  ? 

5.  Read:  DC;  MC;  MCC  ;  CM;  CCXX;  CCCX;  CXXX 

6.  Eead  :  DCCCXX ;  CDXXX  ;  CCLXI ;  CXLVITI. 

7.  Write  in  Roman :  1000;  500;  300;  400;  600;  900 
a  Write  in  Roman :  140;  260;  320;  550;  450;   195 


ritU 

m                               MISCELLANEOUS 

117 

1. 

See  how  quickly  you  can  get  correct  sums : 

a. 

$173.25       b.   $  836.42       c.    $7000.42       d.     497 

92.47              1521.50 

83.92            6839 

9.38                936.08 

6214.83             709 

407.25                  42.53 

807.15             598 

92.16              1006.27 

78.26             763 

57.84                  83.44 

9287.42            6908 

9.26                  64.29 

383.52         89718 

2. 

Find  the  missing  numbers.     Test  your  work : 

a. 

645071          b.     48356           c. 

58605     d.        ? 

-280693              +      ? 

-      ?               x59 

?                      97403 

29567            708 

3. 

Solve  in  figures  DCLIX  x  CCXII. 

4. 

273018-3        io.    362416-4 

is.    342x290 

5. 

452124-*- 3         ii.    122028-4 

17.    4506x206 

6. 

151824-3        12.    253540-5 

is.    1928x453 

7. 

4243x260         13.    312x600 

19.    364218-*- 6 

8. 

4506x206         14.    3424x60 

20.    4530-5 

9. 

192x453           is.    3642-6 

2i.    3206x700 

22.  Find,  the  number  of  square  inches  in  a  rectangle 
98  hi.  by  70  in. 

23.  A  rectangle  contains  1710  sq.  in.     It  is  30  in.  wide. 
How  long  is  it  ? 

24.  The  product  is  6447,  one  factor  is  21.     Find  the 
other.     Make  a  problem. 

25.  392x508  26.    36048-8  27.    875x900 


118  PROBLEMS  Oral 

1.  In  17  pt.  there  are qt.  and pt. 

2.  In  23  qt.  there  are gal.  and pt. 

3.  In  34  qt.  there  are pk.  and pt. 

4.  3  ft.  and  2  in.  are in.     3x12  +  2  = . 

5.  In  39  pk.  there  are bu.  and pk. 

6.  Wilfred  picked  3  pk.  6  qt.  of  cherries.     How  many 
quarts  did  he  pick  ? 

7.  I  bought  a  piece  of  rope  36  ft.  long  and  used  §  of  it 
for  a  swing.     How  many  feet  of  rope  did  I  use  ? 

8.  Harold  picked  a  peck  basket  full  of  apples  29  times. 
How  many  bushels  did  he  pick  and  how  many  pecks  over  ? 

9.  If  your  tablet  is  8  in.  by  10  in.,  how  many  inch 
squares  can  you  make  on  one  page  ? 

Written 

1.  One   box  holds   2  dozen   lemons,  and   another   37 
lemons.     How  many  lemons  in  both  boxes? 

2.  At  $  .05  an  ounce,  what  will  2  lb.  of  candy  cost  ? 

3.  Find  the  cost  of  24  gal.  of  ink  at  12^  a  pint. 

4.  12  gal.  3  qt.  of  maple' sirup  at  25^  a  quart  would 
cost  how  much  ? 

5.  A  man  bought  coal  for  $  4.75  and  wood  for  $  3.50. 
How  much  change  should  he  receive  from  a  $  20  bill  ? 

6.  April,  June,  September,  and  November  have  each 
30  days.     How  many  hours  in  these  months  all  together  ? 

7.  What  is  the  cost  of  288  oranges  at  36  cents  a  dozen  ? 

8.  What  number  multiplied  by  70  will  make  1330  ? 


Oral  MULTIPLICATION  119 

1.  When  steak  costs  18^  a  pound,  a  half  pound  costs 
cents.     1J  pounds  cost  9j^  + 18^  or cents. 

What  would  21  pounds  cost  ?     3  J  pounds  ? 

2.  When  sugar  is  6  cents  a  pound,  3^  pounds  cost  3| 

times  6  cents,  or cents.      (3  x  6  =  18.      J  of  6  =  3. 

18  +  3  =  ?) 

3.  What  is  the  cost  of  41  gal.  of  oil  at  12  ^  a  gallon  ? 

4.  How  many  feet  in  7  yd.  ?     In  \  yd.  ?     In  7f  yd.  ? 

5.  In  1  da.  there  are  hr.     In  f  da.  there  are 


hr.     In  If  da.  there  are hr. 


Written 
1.    How  many  hours  are  there  in  9f  days? 
24 


Q2 

16  hr.  inf  da.  (f  of  24  =  16) 

216  hr.  in  9  da. 

232  hr.  in  9-|  da.     Answer. 

2. 

Find  how  many  hours  in  2  If  days. 

3. 

32 

4.    21          5.    485        6.    485 

7.    485 

x5f 

x8|              xli            xlf 

x7f 

8. 

252 

9.    252      10.    252      ii.     84 

12.   24 

xl{ 

x  If            x  5f          x  16i 

x7# 

13. 

205 

14.    336      is.    485      is.    204 

17.    136 

x9f 

x  6£            x  4f            x  8i 

x2| 

120  MISCELLANEOUS  Oral 

i.  How  many  hours  in  90  minutes  ? 

2.  How  many  seconds  in  2J  minutes  ? 

3.  What  will  3  qt.  of  vinegar  cost  at  $.20  a  gallon  ? 

4.  Give  the  multiplication  tables  of  7,  8,  and  9. 

5.  Give  the  division  tables  of  7,  8,  and  9. 

6.  Give  the  multiplication  tables  of  10,  11,  and  12. 

7.  Give  the  division  tables  of  10,  11,  and  12. 

8.  How  many  pecks  in  3  bu.  3  pk.  ? 

9.  How  many  quarts  in  3  pk.  3  qt.  ? 

io.    What  will  18  lemons  cost  at  $.24  a  dozen ? 
li.    George  sold  10  White  Leghorn  eggs  and  14  Plym- 
outh Rock  eggs  at  $.30  a  dozen.     How  much  did  he 
receive  for  them? 
Written 

i.    Divide  8487  by  41. 
207 

41Jo4o7         28  tens  will  not  contain  41  any  tens'  times,  so  we 
82         put  0  in  tens'  place  in  the  quotient  and- bring  down 
287   ^  units.     287  contains  41  seven  times. 

287 

In  these  examples,  think  first  ivhat  the  guide  figure  is: 

2.  21112-52         5.    70224-28         8.      56160-27 

3.  61676-68  6.      5377-19         9.    399294-42 

4.  41457-39  7.    21137-23        io.    470564-*- 94 
n.    How  many  ounces  in  6J  lb.  ? 

12.    Subtract  the  sum  of  486  and  296  from  1000. 


Written  MISCELLANEOUS  121 

1.  Albert  has  $42  in  the  bank.  Franz  has  2 J  times 
as  much.  a.  How  many  dollars  has  Franz  ?  b.  How 
many  dollars  have  both  ? 

2.  A  boy  whose  age  is  now  12  years  was  born  in  what 
year? 

3.  If  a  boy  earns  $  .48  in  a  week,  what  does  he  earn 
in  9  days  at  the  same  rate  ? 

4.  If  a  dozen  pencils  cost  18  cents,  what  must  be  paid 
for  a  box  holding  6  dozen  pencils  ?     For  4  boxes  ? 

5.  A  fruit  dealer  bought  32  boxes  of  berries  for  $2.56. 
a.  How  much  did  1  box  cost  ?  b.  He  sold  them  at  10  0 
a  box.  Did  he  gain  or  lose,  and  how  much  on  1  box  ? 
c.  On  all  the  boxes  ? 

6.  A  lame  boy  rode  on  the  car  to  and  from  school  every 
day.  His  fare  was  3  cents  each  way.  a.  What  was  his 
car  fare  for  a  week  ?  b.  If  he  was  absent  5  days  in  a 
term  of  20  weeks,  how  much  was  his  car  fare  for  the  term  ? 

7.  If  a  street  car  makes  15  trips  a  day  and  carries  45 
passengers  each  trip,  how  many  passengers  are  carried 
during  the  day  ? 

8.  Columbus  discovered  America  in  the  year  1492. 
How  long  ago  was  that? 

9.  If  a  man  earns  $95  a  month  and  spends  $35  a 
month,  how  much  does  he  save  in  a  year  ? 

10.    31  and  13  are  the  factors  of  what  number? 
li.    A   door  mat  24  in.  by  36  in.  covers  how   many 
square  inches  of  the  floor  ? 


122 


HALVES,  FOURTHS,   AND  EIGHTHS 


i 

i 
X  i 

i 

i 

i 

T 

1 

1 

1 

1 

1 

1 

1 

'I' 

1 

1 

i.    How  many  inch  spaces  are  there  on  this  rule  ?     How- 
many  half-inch  spaces  in  1  inch  ?     In  the  whole  rule  ? 

2.    How  many  %4nch  spaces  in  1  inch  ?     In  the  whole 
rule  ?     In  ^  inch  ?     How  many  quarters  in  an  inch  ? 

How  many  -|-inch  spaces  in  1  inch  ?     In  the  whole 
inch? 


3. 

rule? 


In  1  inch  ? 


W 


4. 


1  inch  =  how   many   half  inches  f     How 


many  \ 


1  inch  =  |  =  |  =  f 


inches  f     How  many  ^  inches  f 

5.    How  many  quarter  inches  in  one  half  inch  ? 


How 


many  £  inches  in  one  half  inch  ?     \  inch  =  J  =  \. 

6.  How  many  \  inches  in  \  inch  ?     \  inch  =  l. 

7.  Two  half  inches   are   how   many  inches?     4   half 
inches  ?     6  half  inches  ? .   8  half  inches  ?     3  half  inches  ? 

8-   f  =  i;  t  =  ^5  f  make  what;  f  =  i 


I-  make  what  ? 


9. 
10. 
11. 
12. 
13. 


J  inch  and  \  inch  make  £  inch ; 

\  inch  and  \  inch  make  I  inch  ;  i  +  i  =  ? 


1  4- 1—  9 

2  +  4"  * 


inch  make  |-  inch 


2^8* 


L  inch  and  -^ 

J  inch  and  1  inch  make  £  inch;  }+£»£. 


Which  is  greater  \  or  i  ? 


iorl?  lor 


i?  i 


or  f  ? 


Oral  MISCELLANEOUS  123 

1.  On  the  rule  (p.  122),  find  $  +  f;  J+J;  i+|; 
ll  +  |;  31  +  1;  11  +  21 

Note.  —  Children  use  their  own  rules  also. 
2     Find  11  +  1-  14  +  24-  144-4*  1^4-1-  "U4.1 

3.  Find  If,  then  take  away  J.     What  is  left  ? 

4.  Find  2|,  then  take  away  -|.     What  is  left  ? 

5.  2  +  3  =  ?    l  +  i  =  ?    2i  +  3i  =  ?   1  +  1  =  ?    5i  +  i=? 

6.  |  +  i  =  ?  6  +  2  =  ?  6|+'2i  =  ?  5f-i  =  ?  7i-i  =  ? 

7.  Mary  has  a  hand  mirror  4  in.  by  6^  in.  How 
many  square  inches  does  it  contain  ?     (Picture.) 

8.  If  the  mirror  was  3  in.  wide  and  contained  15  sq. 
in.,  how  long  would  it  be  ?     (Picture.) 

9.  A  traveler  paid  $.25  for  breakfast,  $.50  for  din- 
ner, $.25  for  supper,  and  $.50  for  lodging.  What  did 
his  board  and  lodging  for  the  day  cost  him  ? 

10.  If  5  pears  cost  15  cents,  10  pears  will  cost  twice  as 
much,  or  cents.     Why  ? 

11.  20   pencils  cost  60  cents.     Five  pencils  cost  \  as 

much,  or cents.     Why  ?     In  what  other  way  could 

you  get  it  ? 

12.  If  2  quarts  of  milk  cost  10  cents,  2  gallons  would 
cost times  as  much,  or cents.     Why  ? 

13.  Henry  earned    40  cents  in  5   hours.     How  much 
could  he  earn  in  10  hours  ?     Find  it  in  two  ways. 

14.  Grace  can  solve  4  problems  in  12  minutes.     How 
many  can  she  solve  in  48  minutes  ?     Find  it  in  two  ways. 

15.  At  2  cents  a  foot,  what  will  6  yd.  2  ft.  of  rope  cost  ? 


124  READING   AND   WRITING  NUMBERS 


423,578,600  is  read,  four  hundred  tiventy-three  million 
five  hundred  seventy-eight  thousand  six  hundred. 

i.    Bead:     125,791,235;      26,625,130;      4,310,240; 
99,000,000;    600,329,842;    100,000,125;    96,000,050. 

Find  results  and  read  them: 

2.  Multiply  by  10 :  14;  28;  79;  192;  345. 

3.  Multiply  by  100  :  210;  980;  6004;  4250. 

4.  Multiply  by  1000 :  13;  25;  49;  324;  20. 

5.  Divide  by  1000:  98,000;  1,239,000;  4,900,000. 

6.  569x3200  12.    2038x490 

7.  423x600  is.    950x2400 

s.  507x500  14.  3,812,400-900 

9.  938x240  is.  180,960 -*- 520 

10.  5803x9000  ie.  50,040-60 

11.  256x8500  17.  308,000  +  800 

18.  The  sun  is  92,000,000  miles  from  the  earth,  a.  If 
you  could  travel  toward  the  sun  at  the  rate  of  40  miles 
an  hour,  you  would  have  to  travel  how  many  hours  to 
reach  it  ?  b.  If  you  should  travel  10  hours  a  day,  how 
many  days  must  you  travel  to  reach  the  sun  ? 

19.  It  is  25,000  miles  around  the  earth.  If  you  travel 
50  miles  an  hour,  how  many  hours  must  you  travel  to  go 
around  the  earth  ? 


Written  REVIEW  125 

l.    How  long  will  it  take  you  to  get  correct  sums  f 
a,  837         b.  628      c.  8063       cL     $26.43       e.  $715.30 


2964 

4307 

259 

18.75 

21.86 

418 

526 

8264 

2.93 

9.24 

3825 

8279 

1287 

4.10 

10.16 

842 

428 

428 

128.06 

7.28 

29 

4273 

3064 

563.13 

516.00 

2.  A  jar  of  butter  containing  23|-  lb.  costs  how  much 
at  30  ^  a  pound  ? 

3.  At  $96  a  month,  how  much  can  a  man  earn  in  7J 
months  ? 

4.  How  many  quarts  in  6-J  bushels  ? 

5.  At  $1.28  a  yard,  what  will  3f  yd.  of  cloth  cost? 

6.  How  many  minutes  in  7f  hours  ? 

7.  5000    s.   $40.12    9.    $25.00    10.  $38.42    11.  495 
-479         -37.84         -     ?  +     ?  x  99 

$23.59  $96.39 

Oral 

1.  Name  all  the  letters  used  in  Roman  notation  and 
give  the  value  of  each. 

2.  A  half  inch  and  a  quarter  inch  are  how  many 
quarters  ?     A  half  dollar  and  a  quarter  dollar  ? 

3.  Put  your  pencil  at  the  left  end  of  the  rule  (p.  122). 
Move  it  11  inches  to  the  right.  Move  it  f  inch  farther. 
How  many  inches  have  you  moved  it  ?     1  \  +  f  =  ? 


126  MULTIPLICATION   AND  DIVISION  Oral 

l.  a.  24x10  2.  a.  12x70  3.  a.  46x20 

6.  45x100  6.  16x30  &.  15x40 

c.  16x20  c.  420x20  c.  12x600 

d.  18x20  d.  51x100  d.  15x50 

e.  30x10  6.  7x1000  e.  90x100 
4.  a.  160  +  10  5.  a.  80-40  6.  a.  600-300 

b.  230-10  b.  280-40  b.  800-200 

c.  40-20  c.  250  +  50  c.  1800-900 

d.  80-20  d.  420-70  d.  36000  +  9000 

e.  100  +  20  e.  860  +  20  e.  720  +  120 

7.  A  pail  weighs  If  pounds,  the  cover  \  pound,  and 
the  contents  of  the  pail  20  pounds.  If  you  carry  it,  how 
many  pounds  must  you  carry  ? 

8.  If  George  gained  5f  lb.  during  vacation  and  lost  \ 
lb.  during  the  first  week  of  school,  how  much  heavier  was 
he  then,  than  when  the  vacation  began  ? 

ADDITION    AND   SUBTRACTION 


9.  a. 

2|+i 

10. 

a. 

n+n 

11. 

a. 

2f+9J 

b. 

H  +  H 

b. 

5f  +  li 

b. 

6i-i 

c. 

7i  +  8J 

c. 

2f  +  | 

c. 

7-1 

d. 

4J  +  81 

d. 

7i  +  i 

d. 

8J-31 

e. 

H+i 

e. 

H+n 

e. 

fi3  _  1 
U4        4 

12.   a. 

5J  +  I 

13. 

a- 

81-1 

°2        4 

14. 

a. 

53-29 

b. 

6|  +  H 

b. 

H-t 

b. 

86-79 

c. 

n+i 

c. 

8*  +  ?  = 

8* 

c. 

65-38 

d. 

H  +  H 

d. 

51  +  ?  = 

6 

d. 

59  +  32 

e. 

12J  +  71 

e. 

4f-?  = 

41 

^2 

e. 

86  +  49 

Written 


PERIMETER 


127 


Fig.  1. 


Fig.  3. 


Fig.  5. 


Fig.  2. 

The  sum  of  all  the  sides  of  a 
figure  is  its  perimeter. 

1.  Measure  the  four  sides  of 
Figure  4.  Add  them.  What  is  the 
perimeter  of  Figure  4  ? 

2.  Measure  the  sides  of  Figure 
5.     Find  its  perimeter. 

3.  Find  the  perimeter  of  Figure 
1 ;  of  Figure  3  ;  of  Figure  2. 

4.  Draw  on  the  blackboard  a  square  9  in.  on  a  side. 
a.  Its  perimeter  is  how  many  inches  ?    o.  How  many  feet  ? 

5.  Draw  a  square  whose  perimeter  is  48  in.    How  many 
inches  long  and  wide  must  it  be  ? 

6.  Measure  your  paper  and  find  its  perimeter. 

7.  Draw  on  the  blackboard  a  rectangle  2  ft.  long  and 
6  in.  wide.     Find  its  perimeter. 

8.  A  garden  bed  is  12  ft.  long  and  8  ft.  wide.     Make  a 
drawing  of  it,  using  i  in.  for  1  ft.    What  is  its  perimeter  ? 

&.    A  city  lot  is  150  ft.  long  and  50  ft.  wide.     What  is 
its  perimeter  ?     Draw  it,  using  1  in.  for  50  ft. 


128  MULTIPLICATION  AND  DIVISION    Oral  and  Written 

There  are  2000  pounds  in  one  ton  (T.). 

One  horse  can  draw  a  ton  of  coal.  A  two-horse  load  of 
coal  usually  contains  two  tons.  Farmers  usually  take  to 
market  about  one  ton  of  hay  at  a  load. 

A  large  flagstone  may  weigh  about  one  ton.  Can  you 
name  something  else  that  weighs  about  one  ton  ? 

1.  How  many  pounds  in  2  T.  of  coal  ?  In  1^  tons  ? 
In  12  tons  ?  In  f  of  a  ton  ?  In  J  ton  ?  In  -fa  of  a  ton  ? 
In  6 \  tons  ? 

2.  A  load  of  iron  rails  weighs  3  tons.  The  wagon 
weighs  1250  lb.  The  horses  weigh  2600  lb.  The  bridge 
that  the  load  is  drawn  across  must  be  strong  enough  to 
hold  up pounds. 

3.  A  car  load  of  coal  weighs  28000  lb.  How  many 
wagon  loads  of  2  T.  each  will  it  make  ? 

4.  Mrs.  Allen  bought  a  quarter  of  a  ton  of  coal.  How 
many  poimds  did  she  buy  ? 

5.  A  ton  of  butter  was  packed  in  pails  holding  50  lb. 
each.     How  many  pails  were  used  ? 

6.  20  bales  of  cotton,  each  containing  500  lb.,  weigh 
how  many  pounds  ?     How  many  tons  ? 

7.  1000  lb.  is  what  part  of  a  ton  ?    500  lb.  ?    200  lb.  ? 

8.  How  many  pounds  in  5  T.  ?    7  T.  ?    21  T.  ?    \  T.  ? 

9.  How  many  ounces  in  1  ton  ?     In  7  T.  ?     In  \  T.  ? 

10.  A  ton  of  hay  was  pressed  into  bales  weighing  200 
pounds  apiece,  a.  How  many  bales  were  there  ?  b.  How 
many  such  bales  would  1\  tons  make?     c.  llf  tons  ? 


Oral  DIVISION  129 

1.    Division  is  often  indicated  by  writing  the  dividend 
above  a  line  and  the  divisor  beloiv  the   same  line,  thus : 


¥=12  +  3  =  4;  ¥  =  3;-^-  = ;|f  = ;.¥- • 

2.  Give  the  quotients:  -*/;  ^5  Wi^ifi  W- 

3.  When  the  dividend  does  not  contain  the  divisor  an 
exact  number  of  times,  the  remainder  is  written  over  the 
divisor,  as  a,  fraction,  thus  -3^  =  4§.  This  means  that  there 
are  four  9's  in  38,  and  2  over,  or,  that  the  quotient  of  38 
divided  by  9  is  4f . 

Find  the  quotients :  ^  ;  V" ;  ¥  5  ¥  5  ¥  J  ¥  5  W  5  if 

4.  At  40  cents  a  pound,  what  is  the  cost  of  ^  lb.  of 
peppermints  and  \  lb.  of  lemon  drops  ? 

Written 

i.    Divide  26670  by  35. 
762 

35 1 26670  35  ig  midway  between  30  and  40.    3  is  contained 

245  in  26  eight  times.     4  is  contained  in  26  six  times.     So 

217  the  first  quotient  figure  is  between  6  and  8,  or  7.     In 

210  a  similar  manner  we  get  6  for  the  second  figure  of  the 

^77  quotient. 

70 

2.  8675  +  25  (use  2  and  3  for  guide  figures). 

3.  3082  -4-  46  (use  4  and  5  for  guide  figures). 
Find  the  quotients : 1 

q      1890       1Q      2.788       ,,       3J111       12      1^_4_8_8       ,3      ,5_1  5  9  & 
9*        ¥5  ■LO-        3  4  ***        8  5  ■L^'         4  6  ■L'5-          8  5 

1  Examples  4  to  13  should  be  read,  "  2210  divided  by  65,"  etc. 


130  MULTIPLICATION  AND  DIVISION     Oral  and  Written 

i.  On  the  blackboard,  make  a  square  1  ft.  wide.  How 
long  is  it  ?     What  is  it  called  ?     Describe  a  square  foot. 

2.  Make  a  rectangle  3  ft.  by  7  ft.  How  many  square 
feet  (sq.  ft)  does  it  contain  ?  Mark  off  the  square  feet  in 
the  rectangle. 

3.  How  many  square  feet  in  an  oblong  9  ft.  by  8  ft.  ? 
7  ft.  by  12  ft.  ?     11  ft.  by  12  ft.  ?     6  ft.  by  7  ft.  ? 

4.  Measure  the  length  and  breadth  of  your  schoolroom 
and  find  the  number  of  square  feet  in  the  floor. 

Note.  —  Length  and  breadth  are  dimensions. 

5.  The  floors  in  our  house  are  rectangles  and  have  the 
following  dimensions : 

Reception  room 12    ft.  by  11^  ft. 

Dining  room 13    ft.  by  16    ft. 

Library 18    ft.  by  13    ft. 

Hall 8    ft.  by  18    ft. 

Kitchen 12|  ft.  by  14    ft. 

a.  Find  the  number  of  square  feet  in  each  of  the  floors. 
b.  In  all  the  floors.     Draw  the  hall,  using  J-  in.  for  1  ft. 

6.  Measure  the  top  of  your  desk  and  find  the  number 
of  square  inches  it  contains.     (Omit  fractions.) 

7.  Mr.  Fancher's  sidewalk  is  5  ft.  wide  and  66  ft.  long* 
What  did  it  cost  at  11  ^  per  square  foot? 

8.  What  would  it  cost  to  put  an  oak  floor  in  the  li- 
brary (question  5)  at  17  ^  per  square  foot  ? 

9.  A  skating  rink  98  ft.  by  212  ft.  contains  bow  many 
square  feet  ?     Find  its  perimeter. 


AREA  131 

1.  Hold  your  hands  1  yd.  apart.  Hold  your  hand  one 
yard  above  the  floor.  Without  a  rule,  draw  on  the  black- 
board a  square  one  yard  long.  How  wide  is  it  ?  Measure 
and  correct  it.    What  is  it  called  ?    Describe  a  square  yard, 

2.  The  top  of  your  teacher's  desk  contains  about  how 
many  square  yards  (sq.  yd.)  ? 

3.  Estimate  the  number  of  square  yards  in  the  floor  of 
your  schoolroom.  Measure  and  see  how  nearly  right  you 
are. 

4.  A  courtyard  is  12  yd.  wide  and  43  yd.  long.  How 
much  would  it  cost  to  pave  it  at  $  1\  a  square  yard  ? 

5.  The  number  of  square  units  (square  yards,  square 
feet,  square  inches,  etc.)  that  a  surface  contains  is  its  area. 
How  do  we  find  the  area  of  a  rectangle  ? 

6.  When  the  area  and  one  dimension  of  a  rectangle 
are  given,  how  can  we  find  the  other  dimension  ? 

7.  The  area  of  a  dining  table  is  36  sq.  ft.  Its  width 
is  4  ft.     What  is  its  length  ?     Draw  it,  using  ^  in.  for  1  ft. 

8.  A  pane  of  glass  is  28  in.  by  32  in.  a.  What  is  its 
area?  b.  A  room  with  3  windows,  each  having  2  such 
panes,  has  how  many  square  inches  of  glass  ? 

9.  Measure  a  floor  in  your  house  and  compute  the 
area.     Make  a  drawing,  using  J  in.  for  1  ft. 

10.  There  are  5280  ft.  in  a  mile.  If  a  pavement  is  a 
mile  long  and  50  ft.  wide,  how  many  square  feet  in  it  ? 

li.  A  mile  is  1760  yd.  How  many  square  yards  in  a 
street  1  mile  by  20  yd.  ? 


132 


DIVISION 


Written 


i.    Find  the  value  of  ^3<p. 


599^1   Quotient 


49)29366 
245 
486 
441 


456 

441 

15 


Proof 
599Jf  Quotient 
x  49       Divisor 
5391 
2396 
29351 
+  15  Remainder 


29366  Dividend, 

There  is  a  remainder  of  15,  which  shows  that  29366  is  15  more 
than  the  product  of  599  and  49. 

Find  the  values  of  the  following.  Test  your  work  by 
multiplying  the  whole  number  in  the  quotient  by  the  divisor, 
and  adding  the  remainder. 


2.  ^>p 

10.  A||± 

14.  ^ 

18.  M^ 


LUi 


3.     *ft* 
7>      18  7  3  6 

ii.  J^yu 

15. 
19. 


22. 


26      6  41_8_8 
Zt>.  33 


3J7_5_6_1 
46 

JL06.01 
23.      l^ftM 


4  .2_20_9_ 
*•         18 

«  56803 
«*•  92 

12.  iu^u 

16.  juyyu 

20.  ^\V=- 


642Q 

42 


5 

9 
13 
17 
21. 

25 


9063 
SO 

9650 
~8"7 

8329 
31 


11  988 
14 


Hi1 


29. 


31053 
65 


31.      27_6_8J> 


24.     1W* 
27.     ±1^  28. 

30.     -8^ 

32.  If  47  apples  will  fill  a  peck  measure,  how  many 
peck  measures  will  4356  apples  fill,  and  how  many  apples 
will  be  left  over  ? 

33.  2000  ounces  of  raisins  will  fill  how  many  pound 
packages  ? 


Oral  REVIEW  133 

i.    Count  by  3's  from  2  to  101  and  back. 

2.  33  Brazil  nuts  were  given  to  a  boy  and  his  two  sisters. 
How  many  apiece  had  they,  if  the  nuts  were  divided  equally  ? 

3.  Joseph,  raised  42  ducks  and  sold  15.  How  many 
had  he  left? 

4.  A  half-dollar,  two  quarters,  a  dime,  and  two  nickels 
are  how  much  money  ? 

5.  A  man  earned  $32.  He  paid  $12  for  a  suit  and 
$  9  for  an  overcoat.     How  much  had  he  left  ? 

6.  What  must  be  paid  for  4  dozen  peaches  at  20  each? 

7.  Ilin.-f2iin.  =  ?in.;  $1|+$11  =  ? 

8.  Mr.  Finch  picked  39  plums  and  divided  them 
equally  among  his  three  sons.  How  many  did  Frank  and 
George  receive? 

Written 

i.    $41.72        2.    $86.05        3.    $32.65        4.    $48.37 

x8  x_6  -14.87  -     ? 

$19.48 

5.  A  man  earns  $20  a  week.  If  he  pays  $.95  a  day 
for  board  and  $1.15  a  day  for  other  things,  how  much 
can  he  save  in  a  week  ? 

6.  Divide  the  product  of  27  and  32  by  their  sum. 

7.  A  man  sold  58  cows  at  $38  apiece  and  176  sheep 
at  $  4  apiece.     What  did  he  receive  for  all  ? 

a.    One  factor  of  7659  is  37.     What  is  the  other  ? 

9.  Ajjp  10.    A|§A  ii.    *ftfiP  12«    -W-9 


134  REVIEW  Oral 

i.   A  dressmaker  bought  4J  dozen  buttons.     When  she 
has  used  20  of  them,  how  many  are  left  ? 
19  +  7  +  8  +  6  _9         12  +  6-8, 
10  '  5 

3.  What  does  a  year's  rent  amount  to  at  $  12  a  month  ? 

4.  What  is  the  amount  of  6  months'  rent  at  $120  a 
year  ?     Can  you  find  it  in  two  ways  ? 

5.  3  yd.  of  gas  pipe  at  8  cents  a  foot  cost  how  much  ? 

6.   x =84.     x =132. 

7.  Six  feet  of  chain  at  $.36  a  yard  cost  how  much  ? 

8.  The  multiplicand  is  42,  the  multiplier  2.  What  is 
the  product  ?     Make  a  problem. 

Written 

i.  Mr.  Graves  receives  a  salary  of  $1404  per  year. 
That  is  how  much  a  month  ? 

2.  A  farmer  sold  a  grocer  235  lb.  of  butter  at  $  .24  a 
pound  and  bought  of  the  grocer  a  barrel  of  sugar  for 
(15.75.  Which  man  received  some  money  and  how 
much? 

3.*  How  many  bushels  of  wheat  will  a  farmer  raise  in 
7J  years  if  he  raises  98  bushels  every  year  ? 

4.  A  sidewalk  5  ft.  wide  contains  485  sq.  ft.  How 
long  is  it  ? 

5.  37  and  459  are  the  factors  of  what  number? 

6.  How  many  tons  of  coal  can  be  put  in  a  bin  that 
will  hold  28000  pounds  ? 

7.   Write  in  words  400,216. 


Oral  REVIEW  135 

i.  From  a  piece  of  meat  weighing  30  ounces,  \  of  a 
pound  was  cut.     How  many  ounces  remained  ? 

2.  Hazel  paid  16  cents  for  buttons  at  24  cents  a  dozen. 
How  many  did  she  buy  ?  How  many  could  she  buy  for 
12  cents  ? 

3.  A  rectangle  contains  54  square  yards.  It  is  9  yd. 
long.     Give  the  question. 

4.  Charlotte  practices  music  three  hours  every  day. 
What  part  of  all  the  time  does  she  practice  ? 

5.  What  part  of  a  minute  is  12  seconds  ? 

6.  Give  two  factors  of  63;  of  96;  of  110;  of  32;  of  48. 

7.  Our  family  uses  a  half  gallon  of  milk  every  day  at 
$  .05  a  quart.     Give  the  question  and  answer. 

Written 

i.  Multiply  CLXIX  by  XCV,  expressing  the  work  in 
figures. 

2.  Two  boys  sold  extracts  and  shared  the  profits 
equally.  The  first  week  they  took  in  $17.25.  Their  ex- 
tracts cost  them  $9.55.     How  much  did  each  boy  make  ? 

3.  Mr.  Banker  bought  a  pony  for  $  142,  a  cart  for  $  25, 
a  harness  for  $13.50,  and  robes,  blankets,  etc.,  for  $19.75. 
What  did  they  all  cost  ? 

In  examples  4-13,  find  the  values  and  test  your  work  : 

a,       3486   ,-   97603   fi   15789  n       84936   a       47_6_30 
*•    19    °'  2  3     b*    6  5     '*    9  3     ***    8  8 

q   12903  ,n   12750  ,,   82493   19   28  35  ,,,   4  3  91, 
9-    6  6    10'    12J   **■    5  3     12'    6  2    13*   ^flP 

14.    $459.62- $78.36        is.    463x847 


136  REVIEW  Orai 

i.  Without  measuring,  draw  a  line  4  in.  long ;  measure 
and  correct  it ;    a  line  9  in.  long ;   12  in. ;   2  yd. ;   1^  ft. 

2.  Estimate  the  width  and  height  of  doors,  windows, 
blackboards,  ventilators,  etc.,  then  measure  and  see  who  is 
most  nearly  correct. 

3.  A  bushel  and  9  qt.  are  how  many  quarts  ? 

4.  ^  in.  =  how  many  fourths  of  an  inch  ?     Eighths  ? 

5.  $f  +  $i  =  ?     $A  +  $i  =  ?     liin.  +  2iin.  =  ? 

6.  What  is  the  time  when  the  minute  hand  is  at  IX 
and  the  hour  hand  is  between  XI  and  XII  ?     (Picture.) 

7.  Express  in  words :  MDC;  CDLX;  DCXC. 

Written 

l.    Add  up,  then  down.     Time  yourself: 

a. 


123  i 

!>.  %    6.34 

c.   903 

d. 

4836  e 

.  %   5.86 

12 

83.59 

74 

539 

9.73 

3 

12.70 

973 

46 

81.29 

456 

893.98 

460 

930 

40.00 

89 

24.57 

23 

89 

'  1.72 

45 

806.93 

58 

98  . 

19.38 

2.  Indicate  the  sum  of   921  and   33   divided  by  106. 

3.  Indicate  the  product  of  1728  and  144  less  5184. 

4.  a.   How  many  pounds  in  J-  of  a  ton  of  corn  meal? 
b.   What  is  it  worth  at  %  28.64  a  ton  ? 

5.  When  hops  are  $  .25  a  pound,  what  should  a  farmer 
receive  for  3000  lb.  of  hops  ? 

6.  Find  the  value  of :  a.  H^ ;  6.  ±£f*  ;  c.  **$£*-. 


Oral  REVIEW  137 

1.  What  will  2  yd.  of  cloth  cost  if  6  yd.  cost  48  cents  ? 

2.  If  your  horse  eats  12  qt.  of  oats  a  day,  how  long 
will  1$  bu.  last  ? 

3.  How  many  right  angles  in  11  rectangles  ? 

4.  How  much  must  a  man  put  in  the  bank  each  month 
to  save  $  96  in  a  year  ? 

5.  A  boy  received  a  quarter  of  a  dollar  a  week  for 
driving  a  farmer's  cows  to  pasture.  How  much  could  he 
earn  in  16  weeks? 

6.  A  quart  is  what  part  of  a  gallon  ?     3  quarts  ? 

7.  What  must  be  paid  for  8  cream  puffs  when  4  cost 
12  cents  ?     (Two  ways.) 

8.  It  takes  Willis  5  weeks  to  earn  10  dollars.  In 
what  time  can  he  earn  18  dollars  ? 

Written 

1.  Without  partial  products,  find  83  x  11 ;  421  x  11. 

2.  By  short  division,  find  the  value  of:  a.  W£-j  b.  J^; 

C    4:4:71  .    J    42JL4 
o.     f  i     ,   a.     1]L    . 

3.  If  Mr.  Kent  works  300  days  in  a  year  at  $4  per 
day,  how  much  will  he  earn  in  11  years? 

4.  Without  partial  products,  find:  a.  186  x  12;  b.  435 
xl2;  c.  9128x12. 

5.  By  short  division,  find:  a.  -^f^;  b.  ^^;  c.  *£p. 

6.  How  many  years  and  months  in  964  months  ? 

7.  A  park  is  240  yd.  long.  How  wide  must  it  be  to 
contain  4320  square  yards  ? 


138  REVIEW  Oral 

i.  How  many  feet  in  all  the  sides  of  a  square  yard  ? 
(Draw  it  on  the  blackboard.) 

0       9  9_    .     8  7  __  .     36 .45 

18   ' .  18x  5_ 18h-3_ 

3*     9  ;    9x5  ;    9+  3 

4.  \  .  \  «  \.     Read  80,306  ;  100,100 ;  705,050. 

5.  How  long  and  wide  is  a  square  that  contains  16 
square  inches  ?     (Picture.) 

6.  If  %  10  is  \  of  my  money,  how  much  money  have  I  ? 

7.  Irving  gathered  \  bu.  of  chestnuts  and  Horace 
gathered  5  qt.  more  than  Irving.  How  many  quarts  did 
Horace  gather  ?     How  many  quarts  did  both  gather  ? 

Written 

1.  There  are  XXXI  chapters  in  the  book  of  Proverbs, 
CL  in  the  book  of  Psalms,  and  LXVI  in  the  book  of 
Isaiah.  How  many  more  chapters  are  there  in  the  book 
of  Psalms  than  in  both  the  others  together  ? 

2.  Two  men  start  from  the  same  place.  A  travels  59 
miles  north  and  B  travels  63  miles  south,  a.  How  far 
apart  are  they?  b.  If  they  had  traveled  in  the  same 
direction,  how  far  apart  would  they  have  been.     (Picture.) 

3.  How  much  greater  is  J  of  86,140  than  J  of  it  ? 

4.  27,404  has  what  factor  besides  68  ? 

5.  The  product  is  7488.  The  multiplier  is  96.  Find 
the  multiplicand.     Make  a  problem. 

6.  George  climbed  |  of  the  distance  to  the  top  of  a 
tree  60  feet  high.     How  far  from  the  ground  was  he  ? 


TO  THE  TEACHER  139 

TO   THE   TEACHER 

The  terras  concrete  number  and  abstract  number  have  become 
so  fixed  in  arithmetical  literature  that  their  propriety,  or  even 
their  necessity,  is  scarcely  questioned. 

A  close  examination  into  the  nature  of  number,  however,  con- 
vinces one  that  number  is  essentially  abstract,  and  that  the  name 
or  denomination  affixed  to  a  number  is  no  part  of  the  number 
itself,  and  is  useful  merely  for  the  purpose  of  reference,  or  as  a 
mark  of  identification,  and  therefore  should  not  be  brought 
into  the  mathematical  operations  performed  with  numbers. 

Possibly  the  child's  intuitive  grasp  of  this  truth  has  made 
him  so  prone  to  interchange  the  terms  in  multiplication,  to  find 
the  "number  of  parts"  instead  of  "one  of  the  parts"  in  divi- 
sion, and  to  resist  the  attempt  of  the  teacher  to  make  him  use 
the  larger  number  for  the  multiplier  in  explaining  a  certain 
class  of  problems. 

Is  it  not  possible,  indeed,  to  add  unlike  numbers  ?  Is  it  not 
as  easy  to  add  6  trees  and  7  books  as  to  add  6  trees  and  7  trees  ? 
We  need  only  to  apply  the  sum  to  a  term  sufficiently  general 
and  call  it  13  things  or  13  objects.  In  either  case,  the  process 
of  addition  is  performed  with  the  numbers  6  and  7,  and  not 
with  the  objects  to  which  the  numbers  are  applied. 

Without  prescribing  any  set  form  for  the  analysis  of  prob- 
lems, let  us  suggest  that  much  time  and  tribulation  may  be 
saved  by  such  a  treatment  of  the  fundamental  operations  as  the 
following :  — 

a.  If  an  apple  costs  2  cents  and  a  peach  3  cents,  both  cost 
as  many  cents  as  the  sum  of  2  and.  5,  or  five  cents. 


140  TO  THE  TEACHER 

b.  If  a  boy  earns  5  dollars  and  spends  3  dollars,  he  saves  as 
many  dollars  as  the  difference  between  5  and  3,  or  2  dollars. 

c.  Since  there  are  2  pints  in  1  quart,  20  quarts  are  equal  to 
as  many  pints  as  the  product  of  2  and  20,  or  40  pints. 

d.  Since  there  are  16  ounces  in  1  pound,  32  ounces  are  equal 
to  as  many  pounds  as  the  quotient  of  32  divided  by  16,  or  2 
pounds. 

e.  If  5  pencils  cost  15  cents,  1  pencil  costs  as  many  cents  as 
the  quotient  of  15  divided  by  5,  or  3  cents. 

This  form  of  analysis  recognizes  in  each  case  the  real  nature 
of  number,  namely,  the  "  how-many-ness  "  of  things,  and  also 
the  true  function  of  addition,  subtraction,  multiplication,  and 
division,  as  operations  with  numbers,  not  with  things.  It  avoids 
all  difficulty  as  to  the  likeness  or  unlikeness  of  terms  in  multi- 
plication and  division.  In  every  problem  involving  multiplica- 
tion, the  question  itself  indicates  to  the  pupil  what  unit-name 
is  to  be  attached  to  the  product,  and  he  need  only  observe  that 
he  has  two  factors  to  multiply  in  order  to  determine  the 
numerical  product.  It  is  wholly  immaterial  which  factor  he 
uses  for  the  multiplier,  or  what  unit-name  either  factor  may 
bear.  Likewise,  in  division,  the  pupil  knows  at  the  outset 
what  is  to  be  the  unit-name  of  the  quotient,  and  that  the  divi- 
dend represents  a  product  of  which  the  divisor  is  one  factor, 
and  the  other  factor  is  to  be  found.  Whether  the  dividend 
and  divisor  are  like  or  unlike  numbers  is  of  no  consequence  in 
the  solution  of  the  problem  or  the  determination  of  the  result. 

It  is  well,  however,  to  label  numbers  with  their  unit-names 
for  convenience  in  referring  to  them  while  solving  a  problem 
or  reviewing  the  work. 


ODD  AND  EVEN  NUMBERS  141 

1.  A  number  that  can  be  exactly  divided  by  2  is  an 
even  number,  as,  2,  4,  6,  8,  10. 

A  number  that  cannot  be  exactly  divided  by  2  is  an  odd 
number,  as,  1,  3,  5,  7,  9,  11. 

2.  Divide  98  by  2.     What  is  the  remainder?     What 
kind  of  a  number  is  98  ? 

3.  Divide  97  by  2.     What  is  the  remainder?     What 
kind  of  a  number  is  97  ? 

4.  Write  all  the  odd  numbers  from  1  to  99. 

5.  Write  all  the  even  numbers  to  100. 

6.  What  are  the  unit  figures  in  the  even  numbers? 
In  the  odd  numbers  ? 

7.  At  how  many  figures  of  a  number  must  you  look 
to  tell  whether  it  is  odd  or  even  ? 

8.  Tell  which  of  the  following  numbers  are  odd  and 
which  are  even:  9,  12,  16,  15,  14,  27,  19,  36,  438,  591. 

9.  What  factor  is  always  found  in  an  even  number  ? 

10.    In  what  kind  of  a  number  is  the  factor  2  never 
found  ? 

li.    Tell  which  of  the  following  numbers  are  odd  and 
which  are  even : 

The  number  of 
a.  Pints  in  a  quart.  /.  Inches  in  a  foot. 

6.  Cents  in  a  half  dime.     g.  Quarts  in  J  gal. 

c.  Quarts  in  a  peck.  h.  Eighths  in  J. 

d.  Minutes  in  \  hr.  i.  Square  inches  in  a  5-inch  square 

e.  Hours  in  f  da.  /.  Quarts  in  |  of  a  bushel. 


142  FACTORS  Oral 

We  have  learned  that  the  multiplier  and  multiplicand 
are  factors  of  the  product,  and  that  the  divisor  and  quotient 
are  factors  of  the  dividend.  If  you  have  the  product  and 
one  of  its  factors,  how  can  you  find  the  other  factor  ?  If 
you  have  the  dividend  and  one  of  its  factors,  how  can  you 
find  the  other  factor  ? 

One  of  the  numbers  that  are  multiplied  to  produce  a 
number  is  a  factor  of  that  number. 

So  small  a  number  as  2  has  factors,  for  2x1  =  2.  What 
are  the  factors  of  2  ? 

In  telling  the  factors  of  a  number,  we  do  not  mention 
the  factor  1,  because  1  is  a  factor  of  every  number. 

i.    Give  two  factors  of  6 ;   9 ;   10  ;  14  ;  15 ;  21 ;  25; 
22;  33;  34;  35;  38;  39;  49;  63;  72;  77;  81. 

2.  Of  what  number  are  12  and  11  factors? 

3.  2x3x5  =  ?     Give  three  factors  of  30. 

4.  7x2x5  =  ?     Give  three  factors  of  70. 

5.  Name  all  the  numbers  that  will  divide  9 ;  8 ;  10 ; 
11;  12;  13;  14. 

6.  5  and  2  are  factors  of  30.    What  other  factors  has  30  ? 

7.  Complete  the  following  statements  and  tell  which 
numbers  are  products  and  which  are  factors : 

a.  8  pints  = quarts. 

b.  5  dozen  copy  books  are copy  books. 

c.  4  bushels  = pecks. 

d.  5  apples,  at  2  ct.  each,  cost ct. 

e.  9x =108. 


QUICK  TEST  143 

1.  25x10  =  ? 

2.  Give  two  factors  of  35. 

3.  Write  the  even  numbers  to  20. 

4.  There  are  120  seconds  in  2  minutes.  What  factor 
is  not  given  ? 

5.  A  sheet  of  wrapping  paper  6  ft.  by  21  ft.  contains 
how  many  square  feet  ? 

6.  6§  +  2f  =  what? 

7.  Dan  bought  a  half  peck  of  peanuts  at  5  cents  a 
quart.     Give  the  question  and  answer. 

8.  The  area  of  a  window  shade  is  21  square  feet.  Its 
length  is  7  ft.  Which  number  is  a  product  ?  What  are 
its  factors  ? 

9.  If  you  sleep  f  of  the  time,  how  many  hours  a  day 
do  you  sleep  ? 

10.  20  min.  is  what  part  of  an  hour  ? 

Oral 

Complete  the  following  statements  and  tell  which  num- 
bers are  products  and  which  are  factors : 

11.  32  ounces  are pounds. 

12.  At  $  12  a  week,  a  man  can  earn  %  96  in weeks. 

13.  A  floor  is  12  ft.  long  and  11  ft.  wide.    Its  area  is . 

14.  A  man's  salary  for  10  years  amounts  to  $15000. 
He  receives dollars  per  year. 

15.  At  25  cents  per  week,  Eoger  should  receive  

for  shoveling  Mr.  Abel's  sidewalk  4  weeks. 


144  FACTORS  Oral 

i.  12  is  what  of  4  and  3  ?  When  4  and  3  are  given, 
how  can  you  get  12  ?  When  12  and  4  are  given,  how 
can  you  get  3  ?  When  12  and  3  are  given,  how  can  you 
get  4  ?     4  and  3  are  what  of  12  ? 

2.  At  7  cents  apiece  what  will  5  pineapples  cost  ? 
Which  numbers  are  factors  ?     What  is  the  product  ? 

3.  If  5  pineapples  cost  35  cents,  how  can  you  find  the 
cost  of  1  pineapple  ?  If  1  pineapple  costs  7  cents,  how  can 
you  find  the  number  of  pineapples  that  35  cents  will  buy? 
5  and  7  are  what  of  35  ?     35  is  what  of  5  and  7  ? 

4.  When  two  factors  are  given,  what  do  you  do  to 
find  the  product  ?  When  the  product  and  one  factor  are 
given,  what  do  you  do  to  find  the  other  factor  ? 

In  each  of  the  following  problems,  tell  ivhich  of  the  things 
mentioned  in  question  4  are  given,  and  ivhich  is  to  be  found : 

5.  What  is  the  area  of  a  rectangle  4  ft.  by  9  ft.  ? 

6.  If  Clarence  earns  12  cents  every  week,  in  how 
many  weeks  will  he  earn  84  cents  ? 

7.  There  are  4  pecks  in  a  bushel.  How  many  pecks 
in  11  bushels  ? 

8.  7  days  make  a  week.     How  many  weeks  in  63  days  ? 

9.  4371-?  =  47.     10.    75x?  =  2025.     11.    38x99  =  ? 

12.  If  $5.10  is  divided  equally  among  3  boys,  how  much 
money  will  each  receive  ? 

13.  An  apple  tree  bore  128  bushels  of  apples  in  16  years. 
That  was  the  same  as  how  many  bushels  in  each  year  ? 

14.  One  factor  of  121  is  11.     What  is  the  other  ? 


Oral  MULTIPLES  145 

i.    2x3  =  ?     6  contains  3  how  many  times  ?     6  con- 
tains 2  how  many  times  ? 

2.  3x5  =  ?     15   contains   3   how   many   times  ?     15 
contains  5  how  many  times  ? 

3.  5x7  =  ?     35    contains    7   how   many   times  ?     35 
contains  5  how  many  times  ? 

4.  44^4  =  ?     44  +  11  =  ?     44  is  what  of  4  and  11  ? 
A   number   that  exactly  contains  another  number  is   a 

multiple  of  that  number. 

5.  Name  a  multiple  of  2  ;  of  3  ;  of  5  ;  of  7  ;  of  4  ;  of  11. 

6.  Name  two  numbers  of  which  6  is  a  multiple. 

7.  Nine  is  a  multiple  of  what  ? 

8.  Every  even  number  is  a  multiple  of  what  ? 

9.  A  number  that  is  not  a  multiple  of  2  is  what  kind 
of  a  number  ? 

10.    6  is  a  multiple  of  what  two  numbers  ? 
li.    Give  all  the  multiples  of  2  up  to  30. 

12.  Give  all  the  multiples  of  3  up  to  36  ;  of  5  up  to  60 ; 
of  4  up  to  48 ;  of  6  up  to  72 ;  of  7  up  to  84. 

13.  How  many  different  numbers  will  divide  36  ? 

14.  The  number  of  cents  that  8  tops  will  cost  at  5^ 
apiece  is  a  multiple  of  what  ? 

15.  77  is  a  multiple  of  7.  It  is  a  multiple  of  what 
other  number  ? 

16.  What  is  the  smallest  number  of  apples  that  you 
could  divide  equally  among  either  3  boys  or  2  boys  with- 
out cutting  any  of  the  apples  ? 


146  FRACTIONS  Oral 

i.    Review  page  122. 

2.  Florence  bought  £  lb.  of  caramels,  \  lb.  of  pepper- 
mints, and  \  lb.  of  butter  scotch.  How  many  pounds  of 
candy  did  she  buy  ? 

3.  What  are  10  jackknives  worth  at  %\  apiece  ? 

4.  What  are  20  knives  worth  at  %  \  apiece  ? 

5.  Cut  a  pie  into  8  equal  pieces.  What  part  oi  the 
pie  is  1  piece  ?     (Picture.) 

How  many  pies,  each  cut  into  8  pieces,  are  needed  to 
serve  24  people  ?     -^  =  ? 

6.  Cut  a  pie  into  quarters.  Give  a  piece  to  each  of 
two  boys.  What  part  of  the  pie  is  gone  ?  What  part  is 
left?    (Picture.)     f  =  ? 

7.  Give  half  a  pie  to  John  and  \  to  Nellie.  What 
part  is  gone  ?     What  part  is  left  ?     (Picture.)     \  =  p 

8.  Cut  a  pie  into  8  pieces.  Give  J  to  Henry  (How 
many  pieces  ?)  and  £  to  Frank.  What  part  is  gone  ? 
What  part  is  left  ?     (Picture.)     i  +  i  =  s-  +  ¥  =  ?     i  + 1  =  ? 

Make  a  picture  of  4  pies  cut  into  8ths.  Each  piece 
is  y.  How  many  pies  do  8  pieces  make?  16  pieces? 
24  pieces  ?  32  pieces  ?  f  =  ?  -1/-  =  ?  \2-  =  ?  ^  =  ?  9 
pieces  make  how  many  pies  ?  11  pieces?  13  pieces?  15 
pieces?  31  pieces?  |=?  ^=?  \5"  =  ?  ¥=?  ¥'  =  ? 
10  pieces  are  how  many  pies?  12  pieces?  18  pieces? 
20  pieces?  28  pieces?  -V°  =  ?  ¥  =  ?  ¥=?  ¥  =  ? 
How  many  pieces  in  \  of  a  pie  ?     ^  ?     |-  ?     J  =  £     J  =  i- 


Oral  FRACTIONS  147 

The  number  written  above  the  line  in  a  fraction  is  the 
numerator. 

The  number  written  below  the  line  in  a  fraction  is  the 
denominator. 

Name  the  numerator  and  the  denominator  of  ^;  f ;  J;  |-. 

The  numerator  and  denominator  are  called  the  terms  of 
a  fraction.     Name  the  terms  of  | ;  ^ ;  ^. 

1.  The  numerator  of  a  fraction  is  5.  The  denominator 
is  9.     What  is  the  fraction  ?     Write  it. 

2.  What  is  the  fraction  whose  numerator  is  8  and 
whose  denominator  is  13  ?     Write  it. 

3.  A  fraction  always  indicates  division.  The  numerator 
is  the  dividend.     The  denominator  is  the  divisor. 

^  =  18-5-9  =  2,   y-  =  17-4-5  =  3f,  |  inch  =  3  inches ^4. 

Draw  a  line  3  in.  long.  Divide  it  into  4  equal  parts. 
Measure  one  part.     How  long  is  it  ? 

Take  3  apples.  Cut  a  quarter  out  of  each  one.  Put 
together  the  3  quarters  cut  out.  What  part  of  an  apple 
do  they  make  ?  How  does  this  compare  with  the  part 
that  is  left  of  each  apple  ?  The  three  apples  have  been 
divided  into  how  many  equal  parts  ? 

4.  Express  as  fractions :  3  -*-  8 ;  7-5-9;  4-f-5;  15-5-3; 
124-4-17. 

18  =  2     18-5-3_9   42  =  9   42-s-2_9   4  =  9   4±4  =  ? 
5*     9        '     9-3      '    14     *    14-*-2         8     '    8h-4 

6.  Write  the  fraction  whose  terms  are  3  and  5 ;  4  and  7 ; 
5  and  8. 


148  FRACTIONS  Oral  and  Written 

1.  A  fraction  whose  terms  cannot  both  be  divided  by 
the  same  number  is  in  its  lowest  terms.  Thus  f  is  in  its 
lowest  terms,  because  2  and  3  cannot  both  be  divided  by 
the  same  number.  |-  is  not  in  its  lowest  terms,  because 
both  4  and  6  can  be  divided  by  the  same  number.  What 
number  will  divide  4  and  6  ? 

2.  Tell  which  of  the  following  fractions  are  in  lowest 
terms : 

h   h    4>    6>    4>    9?    9>    9>    "9>    TIT'    DT>    TT>    A>    T2>    T2# 

3.  Change  £  to  lowest  terms : 

4     4  +  4      1       A 

8  =  8+l  =  2-    An8wer- 

4.  Change  £  to  lowest  terms : 


6  =  6^2  =  ?    AmW6r- 

Change 

to  lowest  terms: 

5. 

3 
6 

6.     f         7.     |         8.    ^ 

9-  A 

10. 

1 

ii. 

A 

12. 

A 

13.     f       14.    T8e      15.    & 

16.    ^ 

17. 

A 

18. 

6 
TIT 

19. 

& 

20-  A  21-  A  22-  A 

ADDITION 

23.    if 

24. 

if 

25. 

M 

l. 

f+ 

4        4        ±#       *  ^  8        8        * 

4    i    1_ 

? 

2. 

1+ 

.2    i    3_8_0         2    i    1    i    2  . 
4+4-4-Z-       5+5+5- 

=*=? 

i  + 

i+l 

+  1 
^2 

=  ? 

3. 

1+ 

4=?       A i 1=?       3.2, 

W  i 

+  i 

=  ? 

4. 

2| 

+  3i  =  5§  =  6.     6J  +  8f  = 

14|=? 

5. 

3| 

+  2i  =  ?     4|  +  5f  =  ?     6i 

+i-? 

6. 

llj 

Ki  =  ?     9f  +  2J  =  ?     7j 

+2f-i 

i 

WHOLE  AND  MIXED  NUMBERS  149 

WHOLE   AND   MIXED   NUMBERS 

A  number  that  is  not  a  fraction  is  a  whole  number. 
Thus,  5,  8,  10,  11,  15,  are  whole  numbers.     Name  others. 

A  ivhole  number  and  a  fraction,  taken  together,  make  a 
mixed  number.     Thus,  21,  7§,  8f ,  are  mixed  numbers. 

The  value  of  a  fraction  whose  numerator  is  larger  than 
its  denominator  is  a  whole  or  a  mixed  number. 

Thus,  |  =  3,  i  =  3i   ^-=4,  ¥  =  2|. 

How  is  the  value  of  a  fraction  found  ? 

"Find   tVip  vfllnp  nf    LP-      2_5       3  9       725      43  2      483 

Tina  me  vaiue  oi  -% -,   -§--,  -y-,  -25-5  jpf-j   "XT* 

Written  * 

i.  Add    341        2.  Add    43f 

42f  581 

56  62-g- 


132f  =  133  Sum  163-11=  164f  Sum 

3.  361   4.  39|   5.  48f  6.   961   7.  235£ 

41f     91f  62  781     342| 

59      85J  t  81f  82J     998_ 

8.  345|   9.  99J   io.  83f  11.   12i   12.  892| 


2961     12|     491      191     4854 
4081     151-     87      388      2073 


3 

4 

3 

_A  J^!l  ^L!_     ouu      ^v,4 

13.   49|   14.  81|   15.  92|   is.  2371   17.  324f 
-26|    -25|    -861    -1951    -197f 

*  Note.  —  Tn  the  answer,  when  the  numerator  of  a  fraction  is  equal  to,  or 
larger  than,  the  denominator,  always  find  the  value  of  the  fraction  as  a 
whole  or  a  mixed  number.     Change  the  fraction  part  to  lowest  terms. 


150  FRACTIONS  Written 

Note.  —  Many  of  these  exercises  may  be  illustrated  by  means  of 
objects  and  drawings. 

l.    Add  |  and  £.  f  =  | 

W 


£  >SWra. 

2. 

Add  f  and  f . 

*• 

-4 

\- 

=1 

Jgi-  =  If  /Swra. 

3. 

Add  12|  and  21|. 

12f  = 

=  12| 

21f  = 

=  21f 

33f  =  34£  Sum. 

4. 

From  18|  take  6J. 

18*' 

-18*. 

H- 

12f  Remainder. 

5. 

Add  \  and  £. 

is.    29f  +  48i 

6. 

Add  \  and  -§-. 

16.    37£  +  81£. 

7. 

Add  f  and  -£. 

17.    57|  +  93f. 

8. 

Add  J  and  J. 

is.    44f  +  65f 

9. 

From  £  take  ^. 

19.    64J  +  23}. 

10. 

From  \  take  -|-. 

20.    91|-42i 

11. 

From  ^  take  J. 

21.    46f-34J. 

12. 

From  |  take  f . 

22.    83£  +  21£. 

13. 

From  £  take  J. 

23.    42|  +  48i 

14. 

From  f  take  J. 

24.    89i  +  40|. 

25.    Alice  bought  9|  yd.  of  silk  and  4J-  yd.  of  muslin. 
How  many  yards  did  she  buy  ? 


Oral  FRACTIONS  151 

I      .1       I ."  .  §       | 

_i_                jl                l_               _L               i                i. 
m.I 2 1 S 1 2 1 2 ^_* h 2 U 

1.  How  many  halves  in  the  line  MN  ? 

2.  How  many  sw^As  in  the  line  MN  ? 

3.  How  many  sixths  in  -|  of  the  line  ?     J  =  -g-. 

4.  Find  jr  more  than  \  of  the  line.  How  many  sixths 
of  the  line  have  you  found  ?     \  +  \  =  §  -f  -J-  =  J. 

5.  Find  f  of  the  line,  f  of  the  line  is  how  much  more 
than  i  of  the  line?     f  ~i  =  f -|  =  f 

6.  When  we  ivish  to  find  the  differences  or  sums  of 
halves  and  sixths,  we  change  the  halves  to  what  ? 

7.  Draw  on  the  blackboard  a  picture  of  a  pie  cut  into 
6  pieces.  Erase  \  of  it.  How  many  halves  are  left  ? 
How  many  sixths  are  left?  Add  f  to  the  part  that  is  left. 
What  part  have  you  ?     -f  +  f  =  ? 

q       1x1-?        l_l__3=?        ij.2  =  ?        5._1=?        4__1  =  ? 
8-2^6^~~*         2^6        •         2^6        *         6        2*        6        2        * 


M> 


i 


\ 


1 

"3" 


9.    \  =  how  many  6ths  ?     f  =  how  many  6ths  ? 
10.    Find  I  and  \  of  the  line.     How  many  6ths  of  the 
line  have  you  found  ? 

11        1_1  —  2._JL  — 1        1  J-  3  _  2    1    3.=  5. 
J"L'      3        6~~  6         6  ~  6*        3  ^  6  ~~  6  ^  6        6* 

i,       lil-?       2.   i    1_?       5_1_?       5_2.  =  ?       3.-1=? 
12'3+F~-        3^6        *        6        3  —  *        6        3        '        6        3 


152  FRACTIONS  Oral 


M. 


1  x  x  x  4 

t  .  6  .  6  6  .  6 


1  4. 

3  '  3 


i 


XT. 


1.  By  what  part  of  the  line  MN  can  you  measure  both 
thirds  and  halves  f  J  =  how  many  sixths  ?  ^  =  how  many 
sixths  ? 

2.  Tb  what  shall  we  change  halves  and  thirds  when  we 
wish  to  find  their  sums  or  differences  f 

3.  Find:  £  +  *;  t+ii  i-1'5  W- 

4.  6-2  =  ?     C  +  3  =  ?     6  is  what  of  2  and  3  ? 


s.   T| 

6. 

3* 

-    4J 

3. 

81 

9.    6| 

1 

3 

§ 

J 

J. 

Subtract : 

io.   2f 

11. 

8* 

12.    91 

13. 

6f 

14.     18f 

J: 

!i 

2* 

J 

Jk 

TFnWen 

i^'nd  results : 

i.    4| 

2. 

15f 

3-     41 

4. 

8f 

s.   47f 

+  81 

+n 

+i 

+  2J 

+i«i 

6.    13f 

7. 

49£ 

s.    99| 

9. 

4321; 

io.    467^ 

-101 

-16f 

-151 

-129* 

-288| 

ritten 

FRACTIONS 

153 

Add: 
i.    181 
16| 

2.    161 
191 

3. 

231 

98| 

4.    54J 
16* 

5.    351 
42| 

6.    17| 

lof 

7.    39£ 
89$ 

8. 

72$ 

811 

9.    46i 

m 

10.    83f 
10| 

ii.    241 
12| 

12.    35f 
19i 

13, 

41i     ; 

181 

u.    70f 
18J 

15.    63§ 
12J 

is.    39f 

12| 

17.    89f 
29i 

18. 

30f     i9.    841 
19i           19| 

20.    97| 
16| 

Find  results 

; 

2i.    481      22.    57| 
-16i          +81| 

23. 

80f      24.    483f 
21|          +239| 

25.    130f 
-21i 

26.    231| 
+  498| 

27.    437J 
+  49£ 

28. 

380£ 
-18| 

29.    421 
-39i 

30.    46f 

+  85| 

Oral 

l.    9-1 

2.    7- 

* 

3.    6- 

"i          * 

H-i 

5.    14-| 

6.    15- 

_3. 

4 

7.    12 

-I         8. 

16-| 

9.    12  -2£ 

io.    14- 

-3* 

ii.    15 

-31       12. 

18-11 

is.    6-2i 

14.     5  — 

if 

15      8- 

5f           16. 

9-2f 

17.    7-1$ 

18.    12- 

-31 

19.     14 

-8f       20. 

12-H| 

154 


FRACTIONS 


Oral 


M. 


i 


f 


* 


"9        I        9 


N. 


1.  ^  =  how  many  ninths  ? 

2.  Find  f  more  than  J.     Can  you  express  it  in  thirds  ? 
How  can  you  express  it  ? 

3.  Express   1    more  than  f.     In  order  to  add  thirds 
and  ninths,  toe  change  the  thirds  to  what  f 

4.  9-3  =  ?     9  is  what  of  3? 


••     t+i- 

10. 

*+f- 

15. 

*+i- — 

a       2.J-* 

11. 

*+*- 

16. 

*-*- — 

6-     S+9- 

'•  i+i 

12. 

*+!= 

17. 

8         2  _ 

9        3- 

8-     i  +  i- 

13. 

*+*- 

18. 

8   •    |  _ 

9  ^  3  ~" 

Q        2    1    1  - 

14. 

1+1= 

19. 

9^3 

9-     f  ^9 

Subtract : 

20.     1       21.     J       22 

1        i 

•     1 
i 

23.     J 

i 

24. 

f       25.     |       26.     | 

i       i       i 

Written 

i.   181  +  171* 

2. 

661  +  14* 

3. 

75f  +  43f 

4.    38f  +  41* 

5. 

341f  +  23i 

6. 

861  +  61* 

7.    191  +  321 

8. 

75f  +  46f 

9. 

73f  +  18| 

10.   lll*  +  211f 

11. 

421$+ 

161 

12. 

39|  +  16i 

13.   88f-43*  " 

14. 

241-141 

15. 

47$ -19$ 

16.   97^-18J 

17. 

125$- 

42* 

18. 

120i-16| 

is.   216$ -19* 

20. 

42|-13i 

21. 

34$ -13* 

Oral  REVIEW  155 

1.  Give  the  factors  of  6 ;  8  ;  9  ;  15 ;  21 ;  33  ;  35  ;  39. 

2.  Name  the  multiples  of  7  to  84. 

3.  What  three  factors,  multiplied  together,  will  pro- 
duce 30  ?     18?     40?     42? 

4.  Give  four  numbers  that  are  factors  of  12. 

5.  A  conductor  took  up  $1.00  in  5-cent  fares.      He 
collected  from  how  many  people  ? 

6.  8  oz.  is  what  part  of  2  lb.  ?  * 

7.  200-10  =  ?        s.    56x10  =  ?       9.   4300-100  =  ? 
10.    3  pk.  3  qt.  are  how  many  qt.  ? 

li.    What  must  be  paid  for  2 \  qt.  of  berries  at  12^  per 
quart  ? 

12.    Even  numbers  are  multiples  of  what  ? 


Written 

1.    Add  up, 

then  down. 

Time 

yourself: 

a.  461 

b. 

$32.15 

c. 

.  9342 

d.  931 

350 

14.63 

8675 

49 

98 

2.75 

4038 

867 

233 

3.81 

5216 

423 

57 

54.29 

7879 

78 

476 

6.38 

4632 

961 

92 

7.93 

184 

28 

2.    436x251  3.    429x807  4.    906x583 

5.    638x246  6.    1132x406         7.    9381x305 

8.    Divide  4725  by  63  and  test  your  work. 


156  PROBLEMS  Oral 

1.  Find  the  cost  of  H  lb.  of  candy  at  2  f  an  ounce. 

2.  Find  the  cost  of  1J-  lb.  of  ginger  at  2^  an  ounce. 

3.  Five  boys  share  equally  1  lb.  9  oz.  of  candy.  What 
is  each  boy's  share  ? 

4.  6  f t.  -}-  2  ft.  +  4  ft.  =  how  many  yards  ? 

5.  How  many  square  inches  in  a  rectangle  6  in.  by 
21  in.?     In  a  rectangle  8  in.  by  3  J  in.? 

6.  Leah  bought  f  yd.  of  muslin  and  used  f  yd.  for  her 
doll.     How  much  remained  ? 

7.  Wallace  gave  J  of  his  candy  to  Charles  and  J-  of  it 
to  Harold.  What  part  of  his  candy  did  he  give  away  ? 
What  part  did  he  keep  ? 

Written 

1.  At  $1.55  a  yard,  what  will  64  yd.  of  carpet  cost? 

2.  Two  boys  skate  in  the  same  direction.  One  goes 
65  yd.,  the  other  3  times  as  far.  How  far  apart  are 
they  ?     (Picture.) 

3.  How  many  yards  and  feet  in  the  perimeter  of  a  floor 
20  ft.  by  15  ft.?     (Picture.) 

4.  Hubert  found  58|-  inches  of  rubber  pipe  and  used 
19J  inches  of  it  for  his  air  pump.     How  much  remained  ? 

5.  A  pine  tree  measures  39|-  in.  around.  Five  years 
ago,  it  measured  28|-  inches.  How  much  has  the  measure 
increased  ? 

6.  If  3f  yd.  of  ribbon  are  cut  from  11J  yd.,  how  much 
remains  ? 


Oral 


FRACTIONS 


157 


M. 


10      I       10      i      10 


10 


^.u^ 


10 


JJL 


1. 


4. 

first  t 

5. 

8. 

11. 


14. 


16. 


18. 


How  many  tenths  are  there  in 


v 


2.    How  many  tenths  in  jr 


i  _  ?   . 

2  ■"  ro  > 


2  _.    ?     . 
5"  ""TO  9 


Inf? 


9 


Inf? 

4  _     ? 
"5~  — T0~* 


Inf? 


5 -ro-> 

7n  order  to  add  fifths  and  halves  what  must  we  do 
10  +  2  =  ?     10  +  5  =  ?     10  is  what  of  5  and  2  ? 


1    .    1  _ 

■F  +o-  — 


+ 


4  _ 


6. 


9. 


.1+2.= 

2  +  5 


1+1= 


TO  4   i 


1_ 

2 


10. 


13. 


4    i    1  _ 
T  +  'fr  — 


*  +  f  — 

4^  +  61  = 


is.    3i  +  5f  = 


17. 


19. 


2  +  5 


11^ 


20.  Frank  shoveled  ^  the  sidewalk  and  Henry  J-  of  it. 
What  part  of  the  walk  was  shoveled  ?  What  part  of  the 
walk  was  not  shoveled  ? 


Written 

i.    235f 
-1871 


2.    307| 
-2991 


3.    799J 
+  609£ 


4.    293f 
+  6171 


s.    9001f 
-8992^ 


6.    83f 
+  791 


7.    4281 
-399f 


s.    5981 
+  2* 


158  REVIEW  AND  PRACTICE  Written 

1.  Harry  took  in  at  his  soda  fountain  on  Monday 
$6.37,  on  Tuesday  $9.14,  on  Wednesday  $6.84,  on 
Thursday  $9.25,  on  Friday  $5.76,  on   Saturday  $7.28. 

a.  How  much  money  did  he  take  in  during  the  week  ? 

b.  Harry's  best  day  was  how  much  better  than  his  poorest 
day? 

2.  A  merchant  bought  a  case  of  pencils  containing  120 
boxes,  each  box  containing  6  dozen  pencils,  a.  How 
many  dozen  were  there?  b.  How  many  pencils  were 
there? 

3.  296£  4.    99$  5.    793f         e.   308£ 
+  549|              +8l|  -24l|  -2091 

7.   435|  8.    895f         9.    973|        10.   43f 

+  79|  +  4081  +461  +  98| 


n.    784^        i2.   46T%        is.   89|  14.   201£ 

+  91f  +78^  +43^  -108f 

15.  Divide  and  test  your  work:  a.  17,745  by  35; 
b.  331,444  by  47;  c.  476,834  by  95;  d.  32,769  by  46/ 

16.  What  number  is  a  multiple  of  436  and  987  ? 

17.  3233  is  a  multiple  of  what  number  besides  53  ? 

18.  Find  a  number  that  is  a  multiple  of  19,  23,  and  41. 

19.  65J-14i=?    20.  42f-13i  =  ?    21.   84|-23£  =  ? 

22.  The  ice  froze  4J-  inches  thick  last  week,  and  5f 
inches  more  this  week.  a.  How  thick  is  it?  b.  If  it 
should  thaw  2J  in.,  how  thick  would  it  then  be? 


Oral  FRACTIONS  159 


M. 


20l   l   l   1   I   I   I   l   l   l   1   I   l   I   1   I   I   I   I   k 


i  i 

J,  i  1  l  X 

1.  How  many  are  there  of  the  smallest  parts  of  the 
line  MN  ?     Each  of  them  is  what  fraction  of  the  line? 

2.  ^=how  many  twentieths?  J  =  how  many  twen- 
tieths? To  what  must  we  change  fourths  and  fifths  in 
order  to  find  their  sums  or  differences  f 

3.  4x5  =  ?     20-5  =  ?     20-4  =  ?     20  is  what  of  4 

ana  O  I      J-^O"?     J~TG>    ~S"~^J5>     4_2(I?     4  —  2TF* 
4.    i+sW       5.    i  +  ^  =  ?       6.    |  +  ^  =  ?       7.    *  +  &-? 
8-    l+i-1  9-    *  +  t  =  ?        10.    i  +  f  =  ?       11.    |  +  i  =  ? 

12.    f  +  J-T        13.    f  +  f  =  ?        14.    f+i-T       15.    f  +  |  =  ? 

Written 

i.   39J  2.   49f  3.   87ft  4.   92£ 

+  46^  +8Lfr  +  46£  +71| 

s.    42f  e.    211ft         7.    149£  s.    21| 

+  89J-  -16f  +|  -14f 

9.    71£  10.    342£         ii.    61f  12.    123£ 

-26^  -187f  +88f  -38| 

13.  915V    14.  109|    15.  482f    is.  821^ 
+  88f       -491     -157£     -1371 


160  PROBLEMS 

Answer  to  yourself  these  questions  about  each  problem  : 
a.  What  is  asked  f  b.  What  is  told  f  c.  What  must  I  find 
first? 

1.  A  liveryman  bought  8  bu.  of  oats  at  $  .40  a  bushel 
and  2  loads  of  hay  at  $12  a  load.     What  did  both  cost? 

2.  Horace  traveled  37  miles  and  Joseph  five  times  as 
far.     How  far  did  both  travel  ?     (Picture.) 

3.  A  farmer  sold  some  butter  for  $47.85,  some  eggs 
for  $5.38,  some  hams  for  $11.57,  and  some  apples  for 
$13.50.  He  put  $53.89  in  the  bank  and  spent  the 
remainder  of  the  money.     How  much  money  did  he  spend? 

4.  Mrs.  Yates  bought  some  coffee  for  48  cents,  some 
sugar  for  65  cents,  and  some  eggs  for  88  cents.  She  gave 
the  clerk  a  $5  bill.  How  much  change  should  he  give 
her? 

5.  A  man  earned  $392  and  used  -f-  of  it.  a.  How 
much  did  he  use  ?     b.  How  much  had  he  left  ? 

6.  8  arithmetics  cost  $4.48.  What  will  16  arithmetics 
cost? 

7.  A  man  earns  $15  a  week  and  saves  J  of  it.  How 
long  will  it  take  him  to  save  $96  ? 

8.  A  man  born  in  1812  died  in  1890.  How  old  was 
he  when  he  died? 

9.  Ted  had  49  marbles  and  Ned  had  four  times  as 
many.     How  many  had  both  ? 

10.  Mrs.  French  bought  38  yards  of  carpet,  and  took 
back  a  piece  54  feet  long.     How  many  yards  did  she  keep  ? 


Oral 


FRACTIONS 


161 


1 
3 

\ — i — i — y 


^ — i — i — i — h 


i 
t 

H — I — r 


1 

5  I 


1.  The  line  MN  is  divided  into  how  many  equal  parts  ? 
What  is  each  of  these  parts  ? 

2.  £  =  how  many  fifteenths  ?    1  =  how  many  fifteenths  ? 


3*     5^  ~  TW> 


5  —  15  9    5  ~  T~5~  >    3"  ~  15- 

4.  3  x  5  =  ?     15  -+•  3  -  ?     15  +  5  =  ?     15  is  what  of 
3  and  5  ? 

5.  To  what  shall  we  change  thirds  and  fifths  so  that  ive 
may  add  or  subtract  them  ? 


fi   1  4_  1  — 
6-  3+T5"- 

o   1  1  2  _ 

in  1  1  2  _ 

—    8. 
11. 
14. 

1 
3 

3 
5 

3 
5 

i 

+  i= 
+*= 
+*- 

1  _ 

9-  3  '  5 

19   1  1  4 

10-  5  '  3  - 

13-  f  +  f=  — 

u   1    2  _ 

12.  3  1  5  - 

,~   1    1  _ 

lj-  5   15  - 

16-  f   15 

J./. 

5 

Written 

i.   31$ 

-25$ 

2.   49$      3. 

+  82$ 

613f 

-127$ 

4. 

412| 
-361f 

5.  912| 

+  87^ 

6.    171      7. 

+  21f 

84f 
+  84$ 

8. 

490f 
-390i| 

9.    Mr.  Ruggles  worked  4|-  months  in  Boston  and  6§ 
months  in  Troy.     How  many  months  did  he  work  ? 


162  REVIEW  AND  PRACTICE  Oral 

1.    *+*-*         2-       f+i-t        3.    i  +  f  =  ?         4.    $  +  *-? 

5.    f  +  f  =  ?         6.       1  +  1  =  ?        7.    l  +  |-  =  ?         8.    1+H? 
9.   f+i-T       10.    7|  +  i  =  ?      11.    i  +  l  =  ?       12.    i-i=? 

is.  f-^-t  «.  A-i-»  is-  A-*=?  is-  *-*-» 

1.  When  36  barrels  of  flour  cost  $140,  what  will  12 
barrels  cost  ? 

2.  A  farmer  received  $240  for  grain,  potatoes,  apples, 
and  chickens.  \  of  the  money  was  for  potatoes,  \  for 
apples,  J  for  grain,  and  the  remainder  for  chickens. 
a.  How  much  did  he  receive  for  grain  ?  b.  For  potatoes  ? 
c.  For  apples  ?     d.  For  chickens  ? 

3.  A  trader  bought  a  horse  for  $150,  and  sold  it  so  as 
to  gain  \  of  the  cost.  a.  What  did  he  gain  ?  b.  For  how 
much  did  he  sell  the  horse  ? 

4.  At  $39  a  head,  how  many  head  of  cattle  can  be 
bought  for  $4173? 

5.  Mr.  Shepherd  sold  132  sheep  to  one  man  for  $  528, 
to  another  man  156  sheep  for  $468,  to  another  man  25 
sheep  for  $  90,  to  another  35  sheep  for  $  140.  a.  How 
many  sheep  were  sold  ?  b.  How  much  was  received  for 
them  ? 

6.  When  $7490  are  paid  for  214  cows,  what  is  the 
cost  of  one  ? 

7.  306f      s.    223f       9.    150f      10.    17f     11.    238| 
+  98f  -161  _1391         +18|         -197| 


Oral 


FRACTIONS 


163 


'         -  A                     4           1 

t                                   3 

jA|A|-A-|A|A|A|A|ife 

1 

3 

12    1     12     |      12    1 

1 

1 
1      1 
12    j 

mi      i      i      i      i      i      i      i      i 

1    .*     I     i     1     i 

1             1             1 

1 

1 

1 

1.  J  of  the  line  MN  is  how  many  twelfths  of  it  ? 

2.  \  of  the  line  MN  is  how  many  twelfths  of  it  ? 

3.  Can  you  find  how  many  twelfths  in  \  of  the  line  ? 
In  i  of  the  line  ? 


4. 


_   ?   .   3_   ?   .5_   ?.jl—   '.   i—   t 

"~  12?    4~T2>    6"  —  T2  >    2~T2>    ¥  _  T2 ' 


5.  ^o  wAa£  sAaZZ  we  change  fourths  and  thirds  in  order 
to  find  their  sums  or  differences  f 

6.  12-^4  =  ?  12-*-3  =  ?  12  is  what  of  4  and  3  ? 
7.12^-2  =  ?  12  +  6  =  ?  12  is  what  of  6  and  2 ? 
8.    Of  what  four  numbers  is  12  a  multiple  ? 

10.  |  =  IV  11.    i  +A  =  ?    12.    |  +  ^  =  ? 


9.  *- 


_    ? 


Tf 


13.  i+  1  =?  14.  |+  1  -?  15.    f  +  J  =?  16.    f  +  f  =? 

»•  l+A"*  18.  4  +  ^  =  ?  19.  ^  +  f  -?  20.  &  +  |  =? 

21.  i"^  =  ?  22.  i~^=?  23.    i  -  1  =?  24.    |  -  £  =? 

25.  |-  i  =?  26.  |-  |   =?  27.    f  -£  =  ?  28.    f  -  &=? 


i.     16} 

6.      14| 
+  93} 


25| 


3. 


43J 


+  17&        -16^ 


4.   84f 


+  18? 


s.   415^ 
-247| 


.   67| 
+  88J 


i.  395f 
-1971 


9.   59^1    lo.   135^ 
+  296| 


-41| 


164  REVIEW  AND  PRACTICE  Oral 

i.  James  gave  J  of  his  marbles  to  one  boy  and  \  to 
another.  What  part  of  his  marbles  did  he  give  away? 
What  part  did  he  keep  ? 

2.  If  Harry  ate  |-  of  a  melon  and  George  \  of  a  melon, 
how  many  melons  did  both  eat  ? 

3.  I  planted  \  of  my  garden  to  corn  and  \  to  potatoes. 
What  part  of  my  garden  is  planted  to  corn  and  potatoes  ? 
Which  crop  occupies  more  of  the  garden  and  how  much 
more? 

4.  10x4  =  20x?     8x3=4x?     3x4=2x? 

5.  If  Harry  has  \  of  a  dollar,  how  much  more  must  he 
obtain  before  he  can  buy  a  $  2  sled  ? 

Written 
l.    Add : 
a. 


61  b.   16& 

c.   13J- 

d.   4J 

«•  91f   /.  12i 

7*    15* 

19J 

H 

14|     8& 

6^     n 

15i 

2& 

8A    7i 

2.  A  garden  75f  ft.  long  and  421  ft.  wide  will  require 
how  many  feet  of  fence  to  inclose  it  ?     (Picture.) 

3.  A  farm  of  108  acres  was  sold  for  $5940.     What 
was  the  selling  price  of  an  acre  ? 

4.  The  battleship  Kansas  is  456  feet  long.      a.  How 
many  yards  long  is  she  ?     b.  How  many  inches  ? 

5.  36  bushels  of  apples  at  75  cents  a  bushel  will  exactly 
pay  for  25  yards  of  cloth  at cents  a  yard. 

6.  10  tons  of  hay  at  $9  a  ton  will  pay  for  18  tons  of 
coal  at  $ per  ton. 


Oral 


FRACTIONS 


165 


i 
i 


M. 


u 


-Ik 


-f 


1.  Into  how  many  equal  parts  is  the  line  MN  divided  ? 
What  is  each  of  those  parts  called  ? 

2.  7  —  14>2~~14>7~Tl~>  T  — Ti~>  T~~  TT>  T~  T4>  T~~T4* 

3.  To  w;7ia£  shall  ive  change  halves  and  sevenths  to  find 
their  sums  or  differences  f 

4.  14-2  =  ?     14-7  =  ?.    14  is  what  of  2  and  7  ? 

5.  W=?    W=?    *-*-»    i+W    *+*«> 

2^7 


i  +  f  = 


2^7 


2^7 


*        2^14        *        2  ^  14        *        7^14        ' 


*+*+&=* 


15} 

28^ 


1401 

139f 

64 


23& 
259f 
1641 


d.  131J|      e. 


87^ 
63f 


981$ 
49^ 
88& 


2.  Subtract  : 

a.   4011 
359| 

&.  71£ 
36f 

c.  731 
15f 

d.   391f 

'   1581 

e.   81$ 

291 

3.  Add  : 

a.   13^    b 
16f 

_4f 

76f 
19| 

5f 

c.  43| 

15| 

71 

'6 

d.   120-iJ 
96} 
14i 

e.  12f 

L4L 

166  REVIEW  AND  PRACTICE  Oral 

i.  Genevieve  had  f  of  an  orange  and  Edith  -|  of  an 
orange.  Which  had  the  greater  part  and  how  much 
greater  ?     (Illustrate.) 

2.  Four  quarts  of  berries  at  9  cents  a  quart  will  pay 
for  how  many  pineapples  at  12  cents  apiece  ? 

3.  A  page  is  8  in.  long  and  contains  40  sq.  in.  How 
wide  is  it  ?     (Draw  it  the  exact  size.) 

4.  Which  is  greater,  f  of  a  dollar  or  J  of  a  dollar  ? 
How  much  greater  ?     (Show  by  picture.) 

5.  3  five-cent  packs  of  firecrackers  and  one  ten-cent 
pack  cost  how  much  ? 

Written 

1.  a.  If  it  takes  $512  to  pay  the  hands  in  a  certain 
factory  for  one  day,  what  will  it  take  to  pay  them  for  one 
week  ?     b.     For  52  weeks  ? 

2.  If  \  lb.  of  tea  costs  22  cents,  what  will  5  lb.  cost  ? 

3.  Take  37^  from  the  sum  of  15 J  and  24J. 

4.  a.  A  half  peck  and  a  half  bushel  of  peanuts  are  how 
many  quarts  ?  b.  How  much  are  they  worth  at  3  cents  a 
pint? 

5.  Divide  the  sum  of  21684f  and  169421  by  19. 

6.  On  the  first  day  of  January,  Kate  had  $  8.52  in  the 
bank  and  deposited  $3.15.  On  the  first  of  March  she 
drew  out  $4.84,  and  on  the  first  of  April  deposited  $5.86. 
She  then  had  how  much  money  in  the  bank  ? 

7.  How  many  pound  cakes  of  sugar  in  17  boxes,  each 
containing  240  cakes  ? 


FRACTIONS  167 

1.  Before  we  find  the  sums  or  differences  of  fourths 

and  halves,  we  change  the  halves  to .     4  is  a  

of  2. 

2.  Before  we  find  the  sums  or  differences  of  fourths  and 
eighths,  we  change  the  fourths  to .     8  is  a of  4. 

3.  Before  we  find  the  sums  or  differences  of  halves 
and  eighths  or  fourths  and  eighths,  we  change  the  halves 
and  fourths  to .     8  is  a of  2  and  4. 

4.  Before  we  find  the  sums  or  differences  of  halves 
and  thirds,  we  change  them  to .     6  is  a of  3  and  2. 

5.  Before  we  find  the  sums  or  differences  of  fifths  and 
thirds,  we  change  them  to .     15  is  a of  5  and  3. 

6.  Before  we  add  halves,  thirds,  fourths,  and  sixths,  we 
change  them  all  to  .     12   is   a  multiple   of  , 

7.  If  you  wish  to  subtract  or  add  sevenths  and  thirds 
you  change  them  to .     is  a  multiple  of  7  and  3. 

21  +  8-t    *-£    21  +  7=?    i  =  a- 

s-  f=<n:    $—A    f=2T    f=2T    4=2T    f=3rr 

9-    ■5T=3'      2T~^      2T-T     ST~T      5I-T     2T-V 
Test:  +  +  &  =  &  +  &-&-* 


Written 

Subtract  and  test  your  work : 


1. 

i-f 

2. 

3  _  1 
T       3 

3. 

1-4 

6. 

t-i 

7. 

5  _  2 
T       3 

8. 

1-1 

4.     W         5.     f-i 
9-     f-J       10-     l-l 


L68  REVIEW  AND  PKACTICE  Oral 

i.    If  an  8-cent  tablet  lasts  you  4  weeks,  what  is  the 
cost  of  your  tablets  for  a  term  of  20  weeks  ? 

2.  What  must  be  paid  for  a  knife  at  30  cents  and  a 
pair  of  skates  at  65  cents  ? 

3.  Change  to  loivest  terms :  £  ;  f ;  f ;  f ;  T2^ ;  § ;  ^ ; 

6.2.3.4.       8.10.        2.       7.       6.       4.       8.12 
T2  >    T2  »    T2  >    T2  9     12  >      12'      14  9     T4  >     14  >     14  >     14  >     1"4  * 

4.  Find  the  value  of  J£;  |;  ^;  ^;  ^;  ^-;  ^;  ^. 

5.  What  is  the  second  multiple  of  12  ?     The  third  ? 

6.  \  of  my  trees  are  apple  trees  and  \  are  cherry  trees. 
What  part  of  all  my  trees  are  apple  and  cherry  ? 

7.  What  is  the  fourth  multiple  of   5?     The  seventh 
multiple  of  9  ?     The  eleventh  multiple  of  12  ? 

8.  What  is  the  smallest  number  that  is  a  multiple  of 
2,  3,  4,  and  5?     Of  2,  4,  8,  and  16  ?    Of  3,  2,  and  5? 

Written 
Add: 

i.  42^   2.  83}   3.  291   4.  49f   5.  196f 
6_5J     41^     68f     84|      25-if 

6.  421|   7.  93|   8.  576   9  18i   ia  6i 
89*     86f      82/T    14|     41 

51     7f 


11.    481      12.    161      13.    851      14.    311  15.    91 
13|             12|             161             53|  lOf 

3.        '     L4I  l!i  67|  12| 

16.    The  rent  of  a  store  is  $840  a  year.  How  much 
rent  must  be  paid  for  the  store  for  3 \  years  ? 


Oral  FRACTIONS  169 

1.  Name  a  number  which  is  a  multiple  of  8  and  3. 

2.  If  we  wish  to  add  or  subtract  eighths  and  thirds,  to 
what  shall  we. change  them? 

3.  Name  all  the  numbers  of  which  24  is  a  multiple. 
What  fractions  other  than  eighths  and  thirds  can  you  add 
or  subtract  by  changing  them  to  24ths? 

*•     1=2*4        3=-h       4=2T       6=A       T2=A* 

-       1_    ?  3_    ?  2—    ?  3_    ?  5__L_         5    —    ? 

5-  2-2~4       ¥-24       "3-21"       4  ~  24       6"~24       12~2¥' 

6-  ¥~24       T2_24        12-24        3  +  8~-        8        12  ""  • 

*•  *+W  i-i=?  i+A=?  |-.*-t  *+&-» 

Written  . 

i.   35£        2.   81£        3.   24J       4.   52J        5.   29|  ' 

+  42|  -37j  +99j  +  49|         -16& 

6.   48^      7.   405ft      s.   48f      9.   479£     10.   405f 
-29|  -98|  +91|        -379|         -399f 

11.   43^     12.    72f     13.   85f     14.   213|     15.   315f 
+  89*         -16£         +88|         -164|         -143|- 


«.  43* 

17.  16JJ 

is.  99f  19.  71f 

20.  63^- 

64* 

19* 

63*    99| 

47^ 

ISA 

22* 

71J     161 

sift 

ISA 

si* 

81TV    141 

*k 

21.   3£+4|  +  5}  =  ?        22.    6f  + 3^+14*  =  ? 
23.   3i  +  3£  +  6*=? 


170  REVIEW  AND  PRACTICE  Written 

i.  From  the  sum  of  4|  and  6J  take  the  sum  of  2^  and 
3*. 

2.  Ben  rode  his  wheel  5f  miles  on  Monday  and  6| 
miles  on  Tuesday.  How  many  miles  did  he  ride  in  the 
two  days  ? 

c.  One  bale  of  hay  weighs  175J  lb.,  another,  186f  lb., 
and  another  199^  lb.  How  many  pounds  do  all  three 
weigh  ? 

4.  A  collector  received  $2f  at  one  house,  $5f  at 
another,  $6J  at  another,  and  $8J  at  another.  How 
much  did  he  receive  ? 

5.  Change  to  lowest  terms  Jt>  ft*  it>  A'  tt>  H 

6.  Find  the  value  of  ^ ;  ±6^ ;  ^^ ;  l||A. 

7.  a.  Find  the  cost  of  35  bushels  of  potatoes  at  58 
cents  a  bushel. 

b.  Find  the  cost  of  19  bushels  of  apples  at  87  cents 
a  bushel. 

c.  Find  the  cost  of  15  boxes  of  peaches  at   35   cents 
a  box. 

d.  Find  the  cost  of  all  three  of  the  above  items. 

8.  Eugene  ran  26^-  rods  while  Charles  ran  25^  rods. 
Which  was  ahead  and  how  much,  if  they  started  together  ? 

9.  a.  How  man)  pounds  of  cotton  in  100  bales,  each 
weighing  480  lb.  ?     b.  How  many  tons  ? 

10.    1000  lb.  is  what  part  of  a  ton  ?     At  $  18  a  ton  what 
is  the  cost  of  1000  lb.  of  hay? 


Oral  FRACTIONS  171 

i.    To  what  would  you  change  ninths  and  halves  if 
you  wished  to  add  or  subtract  them  ? 

2.  What  other  fractions  than  ninths  and  halves  could 
be  added  or  subtracted  by  making  the  same  change  ? 

3.  What  is  the  smallest  number  that  exactly  contains 
2,  3,  6,  and  9  ? 

»       1—    !       1__    f      1-^    ?      1  __    t      2_    ?       2  __    ?       5—    ? 

*•      2  ■    T8>    3  ~  T8>  6  ""  TO?  "9  ~~  TF>  3  ~  TS>   9  ~  I~8>  6       !¥' 

m      4_?       5  _    ?       7  _.    ?       8  _.    ? 
s*     ¥      1T8">   9  —  TB~>  9  ~"  T85  9  ~~  T8 * 

«•  i+A=?  £+&=?  i+H=?  i+H=? 
7.  i+i=?  j-i-?  |+|=?  i+|=?  i+i-? 

a-  #-§-«  *+i=?  W=?   &+W 

i.  39J   2.  316f  3.  45§   4.  88}    s.  486^ 
+  42^   -2151   -27f    +98|    +  3971 

6.  32^  7.  99£   s.  304|  9.  392|  io.  83J 
-28$    +991    -108^   -186&   -47| 

a.  203f  12.  84f  13.  45J  14.  79f   is.  239} 
-107j   +171    -13J    -16f    -175| 

16.  43^  17.  39£  is.  991  19.  43^   20.  8^ 
66H    25^     251     51*      21 

23A    41|     42|     17|      6|_ 

21.  ll|  +  6-|  +  7i  +  3T\  =  ?  22.  4f  +  H  +  2TV  +  3i  =  ? 
23.  5|  +  2i  +  8i  +  4^  =  ?    24.  3i  +  4i  +  5i  +  2i  =  ? 


172  REVIEW  AND  PRACTICE  Oral 

1.  \  pk.  +  -§-  pk.  is  how  many  quarts  ? 

2.  Which  is  greater,  §  of  a  foot  or  f  of  a  foot,  and  how 
much  greater  ? 

3.  Which  is  greater  and  how  much,  J-  of  a  day  or  -|  of 
a  day? 

4.  A  milk  man  sold  a  customer  5  quart  tickets  and  8 
pint  tickets.  How  many  quarts  of  milk  must  he  give  for 
all  the  tickets  ?  How  much  is  it  worth  at  seven  cents  a 
quart? 

5.  When  2  lb.  of  sugar  are  sold  for  9  cents,  what  must 
be  paid  for  8  lb.?     8  lb.  is  how  many  times  2  lb.? 

Written 

i.  A  young  man  earns  $575  a  year.  What  has  he  left 
after  paying  his  board  at  $  15  a  month  ? 

2.  %  8820  was  divided  equally  among  84  Indians.  How 
much  money  did  each  receive  ? 

3.  18  boys  received  each  38  cents  for  distributing  hand- 
bills on  Saturday.     How  much  did  they  all  receive  ? 

4.  Multiply  the  difference  between  6008  and  2119  by  69. 

5.  John  earned  $21,  William  $1|,  and  Henry  $5f. 
How  much  did  all  earn  ? 

6.  A  boy  ate  \  of  a  cocoanut.  What  part  of  the  cocoa- 
nut  was  left  if  he  had  \  of  it  at  first  ? 

7.  The  four  sides  of  a  field  are  33^  rods,  16f  rods,  38f 
rods,  and  41  rods.  How  many  rods  of  fence  will  inclose 
the  field  ? 


FRACTIONS 


173 


1.  Here  are  how  many  pies  ?  Take  away  2  pies.  How 
many  are  left  ?  If  you  take  away  2^  pies,  what  must  you 
do  to  one  of  the  pies  ?  Make  a  picture  of  the  2^  pies  that 
you  take  away.  Make  a  picture  of  the  pies  that  are  left. 
5  pies  less  3  J  pies  are  how  many  pies  ?  5  apples  less  3J 
apples  =  ? 

2.  Make  a  picture  of  5  pies  less  1 J  pies ;  5  pies  less 
If  pies ;  9  pies  less  3 J  pies ;  4  pies  less  1 J  pies ;  5  pies 
less  2-|  pies. 


3.    Froir 

t  5  take  2$. 

5  =4f 
2J-2J 

2|  Remainder. 

4.   83 
-17* 

s.   48 
-19J 

6.    631          7.   7 
-29|          -2| 

8.   431 

-231|- 

9.   423      10.   69      11.   29 


-1921 


-58f 


-9f 


14.   61        is.   46      16.   28 

-A       -if 


-14& 


19.    1  20.    61       2i.    832 

-H  -15f        -731|f 


12. 

401 
-  300f 

17. 

13 

22. 

39 

°9 

-18* 


18.    16 


15*t 


23.   4-87^, 
-48fe  ) 


174  REVIEW  AND  PRACTICE  Oral 

1.  How  many  pounds  in  5  tons  of  coal  ? 

2.  A  man  bought  a  wheelbarrow  for  $3.75  and  paid 
for  it  with  a  $5  bill.     What  change  should  he  receive  ? 

3.  Minnie  had  5  apples  and  gave  If  apples  to  her  sis- 
ter.    How  many  had  she  left  ? 

4.  15^-  barrels  of  water  were  drawn  out  of  a  cistern 
containing  19^  barrels.     How  many  barrels  were  left? 

5.  A  boy  was  four  feet  tall  on  his  ninth  birthday. 
He  had  grown  If  inches  in  a  year.  How  many  inches 
tall  was  he  on  his  eighth  birthday  ? 

Written 

1.  Write  in  words  410,004 ;  203,416  ;  3,000,015. 

2.  Express  in  figures  seven  hundred  six  thousand 
iwenty-nine. 

3.  Write  in  Roman,  451.     Write  in  figures,  CCXI. 

4.  Add     $10.06,     $15.72,    $60.87,    $1.59,    $3.45. 


Add: 

s.  63 

6.  87 

7.  42 

s.  96 

9.  54 

10.  83 

n.  28 

59 

64 

35 

42 

96 

73 

18 

17 

65 

49 

28 

16 

94 

31 

64 

82 

39 

50 

26 

45 

17 

23 

72 

18 

25 

16 

25 

29 

36 

28 

65 

32 

44 

46 

38 

Multiply  : 

12.  896  is.  897  14.  598  is.  384  ie.  999  17.  894 
94     63     76     65    106    200 


OrU  ONXTED  STATES  MONEY  175 

We  have  learned  that  cents  make  one  dime  and 

that dimes  make  one  dollar. 

The  smallest  piece  of  money  used  in  our  country  is  the 
cent,  but  in  making  calculations  we  sometimes  have  to 
speak  of  smaller  amounts  than  one  cent. 

One  tenth  of  a  cent  is  called  a  mill ;  ^  of  a  cent  are 
three  mills ;  ^  of  a  cent  are  seven  mills,  etc.  ^  of  a 
cent  are  how  many  mills  ?     What  part  of  a  cent  are  9 

mills  ?     Since  a  mill  is  ^  of  a  cent, mills  make  one 

cent. 

A  ten-dollar  gold  piece  is  called  an  eagle. 

TABLE  OF  UNITED   STATES   MONEY 


mills  make  1  - 
cents  make  1  - 
dimes  make  1  - 
dollars  make  1 


1.  A  5-cent  piece  is  what  part  of  a  dime  ? 

2.  A  dime  is  what  part  of  a  dollar  ? 

3.  A  50-cent  piece  is  how  many  dimes  ? 

4.  A  2  5-cent  piece  is  how  many  dimes  ? 

5.  How  many  2 5-cent  pieces  are  worth  as  much  as  a 

silver  dollar  ? 

6.  Express  $  1\  as  dollars  and  cents. 

7.  Express  4^  dimes  as  cents. 

8.  A  half  dime,  2  dimes,  a  quarter,  and  a  50-cent  piece 
are  how  many  cents  ?     How  many  dollars  ? 


176  REVIEW  AND  PRACTICE  Written 

l.    A  dairyman  sold  459  lb.  of  cheese  at  $.11  per  pound. 

How  much  did  he  receive  for  it  ? 

459 

He  received  as  many  cents  as  the  product  of  459  and 


11,  or  5049  cents,  which  equals  $  50.49.     Answer. 


$50.49 

2.    1423  bu.  of  peaches  at  $1.25  per  bushel  cost  how 
much? 
1423 

flIJ  -J    op* 

■  71^        $  1.25  =  125  cents.     1423  bu.  of  peaches  at  125  cents 
QQin       a  bushel  cost  as  many  cents  as  the  product  of  1423  and 
1423         125'  0r  177875  cents,  which  equals  $  1778.75.    Answer. 


$1778.75 

3.  What  must  be  paid  for  7  dozen  handkerchiefs  at 
$  1.85  per  dozen  ? 

$  1.85  At  $  1.85  per  dozen,  7  dozen  handkerchiefs  will  cost 

7        as  many  cents  as  the  product  of  185  and  7,  or  1295  cents, 

$12.95         which  equals  $12.95.     Answer. 

Note.  —  From  the  above  examples,  it  is  seen  that  when  either  the 
multiplicand  or  multiplier  contains  cents,  the  product  also  contains 
cents.  We  may  use  either  factor  for  the  multiplier,  pointing  off 
two  places,  for  cents,  in  the  product. 

4.  A  man  bought  a  bushel  of  berries  for  $2.88  and 
sold  them  for  $3.15.  At  that  rate,  how  much  would  he 
gain  on  123  bushels  ? 

5.  Find  the  cost  of  19  lb.  of  coffee  at  $.33  a  pound 
and  134  lb.  of  tea  at  $.56  per  pound. 

Make  problems  and  multiply : 

6.  $4.15      7.    247      s.    $9.36      9.    3456      10.    438 

39  $.05  42  $.98  $.25 


Written  UNITED  STATES  MONEY  177 

i.    Find  the  sums  and  time  yourself: 


a.  $41.36 

6.  $34.63 

c.  $12.98 

d.  $46.89 

52.81 

8.47 

6.32 

4.37 

8.46 

92.45 

4.28 

90.19 

79.38 

3.06 

7.91 

7.81 

8.92 

93.57 

5.16 

6.29 

4.05 

.69 

70.80 

4.38 

2.  Find  ivhat  I  must  pay  for  all  of  these  articles : 

5  boxes  of  note  paper  at  $.25  per  box. 
5  dozen  tablets  at  .50  per  dozen. 

12  paper  weights  at  .19  apiece. 

7  ink  wells  at  .29  apiece. 

3  bottles  of  mucilage  at      .05  per  bottle. 
1  pair  of  scissors  at  .62  per  pair. 

3.  A  merchant  bought  56  yd.  of  silk  for  $43.68. 
a.  What  did  one  yard  cost?     b.  What  did  11  yd.  cost? 

4.  A  farmer  bought  12  sheep  at  $3.75  apiece.  If  he 
sold  them  at  $4.75  apiece,  what  was  his  entire  gain? 

5.  Mr.  Taylor  went  to  Boston.  His  railroad  fare  was 
$8.22  each  way.  He  paid  a  hotel  bill  of  $3.50  per  day 
for  6  days.  His  other  expenses  were  $7.  If  he  started 
with  $  50,  how  much  had  he  left  ? 

6.  A  man  worked  a  week  for  $2.75  per  day.  How 
much  more  did  he  earn  than  enough  to  buy  a  coat  for 
$9.75,  a  vest  for  $1.90,  and  a  hat  for  $2.00  ? 

7.  From  the  sum  of  $4.75  and  $3.74  take  the  sum  of 
$2.38  and  $4.25. 


178  REVIEW   AND  PRACTICE  Oral 

1.  Frank's  mother  made  4  pies.  They  were  cut  into 
quarters,  and  to  each  of  seven  boys  was  given  a  quarter. 
How  many  pies  were  left  ?     (Picture.) 

2.  Susan  found  7  apples  under  the  pippin  tree.  After 
she  had  given  away  4  apples,  and  eaten  |-  of  an  apple,  how 
many  were  left  ? 

3.  What  is  the  7th  multiple  of  12  ?  56  is  the  8th  mul- 
tiple of  what  ?     150  is  the  10th  multiple  of  what  ? 

4.  Give  three  factors  of  20  ;  four  factors  of  16. 

5.  Name  three  numbers  that  will  exactly  divide  28. 

6.  Name  three  numbers  that  will  exactly  contain  5. 

Written 

1.  From  the  sum  of  $12.15  and  $16.48  subtract  the 
sum  of  $10.18  and  $9.50. 

2.  Add  six  hundred  four  thousand  five  hundred  eight 
to  ninety-four  thousand  fifty-six,  and  from  the  sum  sub- 
tract five  hundred  six  thousand  ten. 

3.  A  farmer  had  25  acres  of  corn  which  yielded  55 
bushels  per  acre.  a.  How  many  bushels  of  corn  did  the 
farmer  have?  b.  How  many  pounds  did  it  weigh  if  a 
bushel  weighed  56  pounds  ? 

4.  a.  Find  the  cost  of  5  chickens  at  37  cents  apiece 
and  8  ducks  at  42  cents  each. 

b.  How  much  more  do  the  ducks  cost  than  the  chickens? 

5.  a.  6f  +  4f  +  7f  =  ?     b.  9ii-7f  =  ?     (Problems.) 

6.  Express  in  Roman  696  ;  in  figures  DCXCIV. 


LIQUID  MEASURE  179 

One  fourth  of  a  pint  is  a  gill.  It  is  sometimes  used  in 
measuring  small  quantities  of  liquids.  A  common  teacup 
holds  a  little  less  than  two  gills. 

TABLE   OF  LIQUID  MEASUKE 
gills  (gi.)  make  1  ■ 


pints  (pt.)  make  1 


quarts  (qt.)  make  1 (gal.) 

1.  There  are  how  many  pints  in  a  gallon  ? 

2.  There  are  how  many  gills  in  a  gallon  ? 

3.  Three  quarts  are  what  part  of  a  gallon  ? 

4.  Seven  pints  are  what  part  of  a  gallon  ? 

5.  Five  gills  are  what  part  of  a  gallon  ? 

Written 

1.  A  milkman  sold  19  gal.  of  cream  in  bottles,  each 
holding  2  gi.     How  many  bottles  of  cream  did  he  sell  ? 

2.  One  customer  bought  2  gal.  1  qt.  of  milk,  another 
7  qt.,  and  another  20  pint  bottles.  How  many  quarts  of 
milk  did  they  all  buy  ? 

3.  How  many  gallons  and  quarts  of  vinegar  are  needed 
for  138  cans  of  pickles,  using  1  pt.  of  vinegar  for  each  can " 

4.  Change  to  pints :  a.  17  gal.  3  qt.  o.  51  gal.  1  pt. 
c.  144  gi.     d.  4325  gal. 

5.  Change  to  gallons  :  a.  128  qt.    b.  112  pt.    c.  352  gi. 

6.  How  many  days  will  5  gal.  of  oil  last  an  engineer 
who  uses  1  gi.  every  day  ? 


180  REVIEW  AND   PRACTICE  Oral 

i.  When  a  gallon  of  molasses  is  worth  48  cents,  what 
is  a  pint  worth  ?     Two  quarts  ?     One  gill  ? 

2.  At  24  ^  a  dozen  what  must  be  paid  for  18  eggs  ? 

3.  If  6  plums  cost  a  cent,  how  many  can  be  bought  for 
12  cents? 

4.  3  £  lb.  of  beefsteak  cost  how  much  at  $  .12  per  lb.  ? 

5.  How  many  dollars  must  be  paid  for  15  spelling  books 
at  $  J  apiece  ? 

6.  What  is  the  smallest  number  that  contains  the  factors 
3,  2,  and  5  ?     2,  3,  and  4  ?     5,  4,  10,  and  2  ? 

Written 

i.  A  merchant  sold  3J  yd.  of  velvet  to  one  lady,  4-|  yd. 
to  another,  1^  yd.  to  another,  and  1^  yd.  to  another. 
How  many  yards  of  velvet  did  he  sell  to  all  ? 

2.  Irene  bought  a  handkerchief  for  $  J-,  bead  trimming 
for  $f,  and  a  sailor  hat  for  $1.  a.  What  was  the  entire 
cost  ?     h.  What  change  did  she  receive  for  a  $  5  bill  ? 


3       3  9  7  8 
d-         3  9 

_  9     11704. 
56 

_?     8  9  3  2  _  ? 
29 

148_tl  _  f 
19 

24644  _  9 
61 

4.   Add: 

a.  2\ 

b.  3£ 

c.  92f 

£ 

46£ 

«.  481 

% 

^ 

m 

79A 

82| 

5f 

n 

79f 

48ft 

66i| 

3. 

8* 

641 

80* 

991 

5.    Subtract  and  test 

your  work  : 

a.  39 

b.  401 

c.  98f 

d. 

78f 

e.  435! 

19f 

36i 

21f 

291 

2411 

DRY  MEASURE  181 

TABLE   OF  DKY  MEASURE 

—  pints  (pt.)  make  1 

—  quarts  (qt.)  make  1 


pecks  (pk.)  make  1 (bu.) 

Note.  —  One  quart,  dry  measure,  is  nearly  equal  to  1|  quarts,  liquid 
measure. 

i.    1  bu.  =  pk.  =  qt.  =  pt. 

2.  How  many  quarts  in  1  bu.  ?     In  1  bu.  ?     In  ^  bu.  ? 

3.  Seed  corn  at  2  cents  a  pint  is  how  much  a  quart  ? 

4.  3  quarts  are  what  part  of  a  peck  ? 

5.  A  man  bought  a  bushel  of  beans,  sold  3  pk.,  and 
gave  away  4  qt.     How  many  pints  did  he  keep  ? 

Written 

1.  A  boy  bought  3  bu.  of  peanuts  at  $1.75  per  bushel. 

a.  What  did  they  cost  ?  b.  He  roasted  them  and  sold 
them  at  the  rate  of  5  cents  for  a  pint  cupful.  What  did 
he  receive  ?     c.  How  much  did  he  gain  ? 

2.  a.  In   205    bushels    there    are    how    many    pecks  ? 

b.  How  many  quarts  ?     c.  How  many  pints  ? 

3.  In  435  pt.  there  are :  a.  How  many  quarts  and 
pints?  b.  How  many  pecks,  quarts,  and  pints ?  c.  How 
many  bushels,  pecks,  quarts,  and  pints  ? 

4.  \  bu.  and  \  bu.  are  how  many  pints  ? 

5.  If  8  bu.  of  sweet  potatoes  cost  $6.72,  what  will  1 
peck  cost  at  the  same  rate  ? 

6.  If  my  horse  eats  6  quarts  of  oats  a  day,  how  many 
days  will  12  bushels  of  oats  last  him  ? 


182  REVIEW  AND  PRACTICE  Oral 

i.    An  orchard  has  600  trees  in  20  rows.     How  many 
trees  in  a  row  ? 

2.  To  how  many  girls  could  6  apples  be  given  if  each 
girl  receives  \  of  an  apple  ?     (Illustrate.) 

3.  40  +  30  =  ?    43  +  34  =  ?     35  +  27  =  ?     24  +  29  =  ? 

4.  93-33  =  ?     93-37  =  ?    42-26  =  ?     84-45  =  ? 

5.  \  and  \  of  a  pound  of  sugar  are  what  part  of  a 
pound  ? 

6.  If  there  are  ten  brown  eggs  in  9  dozen  and  the  rest 
are  white,  how  many  are  white  ? 

7.  One  eleventh  of  a  class  of  55  pupils  are  absent. 
How  many  are  present? 

Written 

1.  A  man  received  $2.40  for  eight  hours'  work.    How 
much  did  he  receive  for  three  hours'  work  ? 

2.  800  qt.  are  how  many  bushels  ? 

3.  Where  are  the  hour  and  minute  hands  of  a  clock  at 
half  past  12  ?     (Picture.) 

4.  Express  in  Roman  three  hundred  fifty-four. 

5.  How  many  quart  boxes  can  be  filled  from  38  bushels 
of  peaches  ? 


Add: 
6.   Sf 

7.   4| 

8.  4| 

9.  8f 

10.  %ts 

H 

11J 

H 

7A 

H 

H 

H 

H 

5J 

n 

4A 

8A 

§t 

3| 

8* 

TIME  183 

TABLE   OF   TIME 


seconds  (sec.)  make  1  - 
minutes  (min.)  make  1 
hours  (hr.)  make  1 


days  (da.)  make  1 (wk.) 

months  (mo.)  make  1 (yr.) 


Learn : 


"  Thirty  days  have  September, 
April,  June,  and  November." 

1.  How  many  months  have  30  days  each  ? 

2.  February  has  28  days  in  all  years  but  leap  years. 
How  often  does  leap  year  come  ? 

3.  How  many  days  has  February  in  leap  year  ? 

4.  How  many  months  have  31  days  each  ? 

5.  a.  Write  the  names  of  the  months  in  order  with 
the  number  of  days  in  each.  b.  Which  long  months  are 
not  separated  by  short  months  ? 

6.  How  many  seconds  in  1  hour  ? 

7.  How  many  minutes  in  1^  hr.  ? 

8.  15  min.  is  what  part  of  an  hour  ?  30  min.  ?  45  min.  ? 

9.  There  are  180  minutes  in  a  certain  number  of  hours. 
180  is  the  product  of  60  and . 

10.    2  hours  is  what  part  of  a  day?  3  hr.?  8  hr.?  12  hr.? 

li.  How  many  hours  in  -|  of  a  day  ?  In  f  of  a  day  ? 
In  |-  of  a  day  ?     In  f  of  a  day  ?     In  %  of  a  day  ? 

12.  Twelve  boys  went  to  a  fire  and  were  15  min.  late  at 
school.    How  many  minutes  were  lost  ?    How  many  hours  ? 


184  TIME  Written 

i.  In  the  month  of  September  there  are  how  many 
(a)  hours,    (b)  minutes,   (c)  seconds? 

2.  a.  If  a  clock  pendulum  swings  once  every  second, 
in  how  many  minutes  will  it  swing  1,814,400  times? 
b.  In  how  many  hours  ?  c.  In  how  many  days  ?  d.  In 
how  many  weeks  ? 

3.  The  Spanish  War  was  fought  in  1898.  That  was 
how  many  years  ago  ? 

4.  In  four  years,  February  has  how  many  days  less  than 
January  has  during  the  same  years  ?     Hours  ?     Minutes  ? 

5.  If  you  are  idle  one  fourth  of  the  time  during  eight 
hours  of  every  day,  how  many  hours  do  you  lose  during  a 
year  of  307  working  days  ? 

6.  $  1296  a  year  is  how  many  dollars  a  month  ? 

7.  If  there  are  300  working  days  in  a  year,  how 
much  would  it  cost  to  hire  a  man  for  5  years  at  $3| 
per  day? 

8.  The  President  of  the  United  States  receives  a  salary 
of  $  50,000  per  year.  If  his  expenses  are  $  35,000  per  year, 
how  much  a  month  can  he  save  from  his  salary  ? 

9.  If  a  boy  sells  an  average  of  1  paper  a  minute  for  half 
an  hour  every  day,  at  2  cents  apiece,  how  much  money 
will  he  take  in  during  a  week  ? 

10.    From  noon  until  midnight  is  how  many  minutes? 

li..  March,  April,  and  May  are  the  spring  months. 
September,  October,  and  November  are  the  fall  months. 
Which  is  longer,  spring  or  fall,  and  how  much  ? 


PROBLEMS 


185 


From  photograph  by  A.  P.  Yates. 


i.  This  train  is  called  the  "  20th  Century  Limited." 
It  runs  from  New  York  to  Chicago,  a  distance  of  980 
miles,  in  18  hours,  a.  That  is  an  average  rate  of  how 
many  miles  an  hour  ?  b.  What  part  of  a  day  is  required 
for  the  trip  ?  c.  How  many  minutes  are  required  for  the 
trip  ?  d.  If  the  five  cars  are  each  73  feet  long  and  the 
locomotive  and  tender  together  are  58  ft.  long,  how  long 
is  the  train  ? 

2.  When  this  picture  was  taken,  the  train  was  running 
at  the  rate  of  90  miles  an  hour.  a.  It  was  running  at 
what  rate  per  minute?  b.  How  far  would  it  go  in  20 
min.  at  that  rate? 

3.  a.  Find  the  cost  of  a  ticket  from  New  York  to 
Chicago  at  2^  per  mile.  b.  From  New  York  to  Buffalo 
is  440  miles.     From  Buffalo  to  Chicago  is  how  far  ? 


186 


DIVISiOJN 


Written 


WjlBf? 


1.    Divide  4693  by  100. 

46^  Quotient    4693  =  4600  +  93 
4600-100  =  46 
93-*- 100  =  ^5-     46T9^    Quotient 

Divide  3687  by  40. 

92¥7-0      Quotient     3687  =  3680  +  7 
4PJ368;  3580-40  =  92 


40  =  A 


»2A 


Quotient 


3.    Divide  54,763  by  500. 
109ff£     Quotient     54,763  =  54,700  +  63 


5PP)5470? 


54,700-*- 500  =  109  and  200  over 


4.  149-10 
7.  5638-1000 
io.  9747-50 


263^500  =  fff 
5.  3462-10 
8.  2420-20 
ii.  98,924-40 


is.  947,612-3000  14.  29*305-600 
is.  98,370-5-90        17.  73,462-90 


109fff      Quotient 

6.  84,763-1000 

9.  3742-200 

12.  6807-340 

is.  6350-50 

is.  742,491-6000 


19   14030 
19-    4  6 


21. 


79808 


22. 


162400 
35 


on   17464 

20.    74       *A.    58 

23.  In  examples  19  to  22,  tell  which  numbers  are  prod- 
ucts and  which  are  factors.  When  a  product  and  one  of 
its  two  factors  are  given,  how  can  the  other  factor  be 
found?     70,196  =  92  x? 

24.  A  rifle  range  is  625  yards  long  and  98  yards  wide. 
How  many  square  yards  does  it  contain  ?  The  area  is 
what  of  98  and  625  ?     Find  the  perimeter. 


AVOIRDUPOIS  WEIGHT  187 

TABLE  OF  AVOIRDUPOIS  WEIGHT 

ounces  (oz.)  make  1  pound 

pounds  (lb.)  make  1  ton  (T.) 

1.  Give  the  number  of  ounces  in  J  lb. ;  f  lb. ;  f  lb. 

2.  How  many  ounces  in  1  T.  ? 

3.  How  many  pounds  in  J  T.  ?     In  \  T.  ? 

4.  100  pounds  is  what  part  of  a  ton  ? 

5.  100  pounds  is  sometimes  called  a  hundredweight. 
Cwt.  stands  for  hundredweight.  How  many  hundred- 
weight make  a  ton  ?     \  T.  ?     \%\    f  T.  ? 

6.  What  must  be  paid  for  1  T.  of  hay  at  $  1  per  hun- 
dredweight ? 

7.  If  a  ton  of  coal  cost  $4.00,  what  will  5  cwt.  cost? 

8.  At  $  2  per  hundredweight,  what  will  1  T.  cost  ? 

Written 

1.  How  many  4-ounce  bags  can  I  fill  from  a  box  con- 
taining 7 J?  lb.  of  candy  ? 

2.  I  had  12  T.  of  coal  delivered  in  bags  holding  100  lb. 
apiece.     How  many  bags  of  coal  were  there  ? 

3.  A  wagon  contained  a  ton  of  coal.  J-  of  it  was  de- 
livered to  Mr.  A.  and  450  lb.  to  Mr.  B.  a.  How  many 
pounds  did  Mr.  A.  receive  ?  b.  How  many  pounds  re- 
mained in  the  wagon? 

4.  If  there  are  80  pieces  of  baggage  in  the  baggage  car 
(p.  185),  weighing  an  average  of  50  lb.  apiece,  how  many 
tons  does  the  baggage  weigh  ? 


188  LINEAR  MEASURE 

THE  TABLE   OF   LINEAR   MEASURE 

12  inches  (in. )  make  1  foot. 

3  feet  (ft. )  make  1  yard. 

5|  yards  (yd.)  1 

or  >  make  1  rod. 

16|  feet  J 


320  rods  (rd.)  make  1  mile  (mi.). 


Oral 


1.  The  longest  boards  commonly  used  for  floors,  siding, 
etc.,  are  16  feet  long.  They  are  how  much  less  than  a 
rod  long  ?     They  are  how  many  yards  and  feet  long  ? 

2.  Measure  a  rod  on  the  floor  with  a  foot  rule,  and 
then  with  a  yardstick.  Draw  on  the  blackboard  a  line  that 
you  think  is  1  rod  long.  Measure  and  correct  it.  Esti- 
mate and  measure  various  distances,  as  the  length  and 
breadth  of  the  school  lot,  the  distance  to  the  nearest 
corner,  etc. 

3.  A  city  lot  3  rods  wide  is  how  many  feet  wide  ?  A 
city  lot  4  rods  wide  is  how  many  feet  wide  ? 

4.  A  city  lot  8  rods  long  is  how  many  feet  long  ? 

5.  Knowing  that  5^  yd.  make  1  rod,  how  could  you 
prove  that  16^  feet  make  one  rod  ? 

6.  A  short  city  block  is  about  20  rd.  long.  How  many 
such  blocks  would  make  a  mile  ?  If  the  blocks  were  twice 
as  long,  how  many  blocks  would  make  a  walk  of  1  mile  ? 

7.  How  many  feet  of  moulding  will  make  a  picture 
frame  36  in.  by  24  in?     Make  a  drawing. 


Written  LINEAR  MEASURE  189 

i.  Find  the  number  of  feet  in 
one  mileo 

2.  How  many  ties  are  needed  for 
a  mile  of  railroad  track,  if  they  are 
laid  two  feet  apart,  from  center  to 
center  ? 

3.  If  a  man's  steps  are  each  three 
feet  long,  how  many  steps  will  he  take  in  walking   1± 
miles  ? 

4.  A  field  is  in  the  shape  of  a  rectangle  44  rods  by  68 
rods.  How  many  rods  of  fence  are  needed  to  inclose  it  ? 
(Picture.) 


5. 

a. 

How 

many 

feet  in  J 

mi.? 

6. 

In 

1 

mi.? 

c. 

In 

l 

mi.? 

d. 

Inl 

mi.? 

e.  In  £ 

mi.  ? 

/• 

In 

7 
H 

mi.? 

9* 

In 

5 

G 

mi.? 

h. 

Inf 

mi.  ? 

i.  In  6| 

mi.? 

6.  A  16-foot  wire  could  be  cut  into  how  many  1-inch 
pieces  ? 

7.  How  many  yards  of  matting  would  be  needed  to 
reach  the  length  of  a  hall  that  is  87  ft.  long  ? 

8.  A  man  bought  a  rope  66  ft.  long.  He  cut  off  and 
used  \  of  it  ?     How  many  inches  of  rope  were  left  ? 

9.  A  race  track,  shaped  like  a  zero,  is  80  rods  around. 
a.  How  many  times  must  a  runner  go  around  the  track  to 
run  2  miles?  b.  How  many  miles  does  he  run  in  going 
around  the  track  32  times  ? 

10.  How  many  yards  make  a  mile  ? 

11.  How  many  inches  in  a  mile  ? 

12.  How  many  inches  in  -|  of  a  mile  ? 


190  REVIEW   AND  PRACTICE  Written 

i.  What  is  the  cost  of  42  yd.  of  carpet  at  $.75  a 
yard  ? 

2.  A  peach  orchard  contains  625  trees  in  25  equal 
rows. 

a.  How  many  trees  in  each  row  ? 

b.  If  each  tree  bears  168  peaches,  how  many  peaches 
do  all  the  trees  bear? 

c.  How  many  baskets,  each  holding  28  peaches,  will 
contain  the  crop  ? 

d.  If  they  are  shipped  in  crates,  each  holding  6  baskets, 
how  many  crates  are  needed  ? 

e.  What  are  the  peaches  worth  at  95  cents  a  crate  ? 

3.  Mr.  Blank  earns  $  96  a  month  and  his  expenses  are 
$  58  a  month,  a.  How  much  can  he  save  in  1  year  ? 
b.    How  much  can  he  save  in  25  years  ? 

4.  How  many  hundredweight  of  coal  in  25  tons  ? 

5.  John  was  born  in  1888  and  Ethel  in  1897.  a.  How 
old  is  each  now  ?     b.  John  is  how  much  older  than  Ethel  ? 

6.  If  a  clock  gains  2  min.  every  day,  in  how  many 
days  will  it  gain  1  \  hours  ? 

7.  How  many  hundredweight  in  27  tons  ? 

8.  a.  How  many  feet  in  48  rods?  b.  How  many 
yards  ? 

J"L'2^5^10^2lT-  iZ'20        5        * 

13.     136-19f-=?  14.     f-f=? 

_    803  +  796     9  647-256     9  72  x  54     , 

15. =  i       16.     =  i       17.     =  i 

39  23  12 


Written  DIVISION  191 

i.    Divide  495,018  by  534. 
927  Quotient. 
534)495018 
4806 
1441  We  get  the  quotient  figures  by  saying,  "How 

1068         many  5's  in  49,  in  14,  in  37  ?  " 

3738 
3738 
Test  every  example  by  multiplication. 

2.  Divide  84,148  by  193.     What  will  be  your  guide 
figure  ? 

3.  Divide  410,032  by  523. 

4.  Divide  18,432  by  512. 

5.  Divide  183,513  by  913. 
Find  the  value : 

io.   *£fta        11.   A^J.        12-   W         13.   *u^ 

14.    *m&         «•    "^gii^         «•    ^We41     "■    ^fF 

.Fmd  quotients  and  remainders : 
is.  12,324  +  213       19.32,634  +  111       20.    22,724-*- 437 
21.23,919  +  119       22.18,647  +  29  23.    11,502  +  309 

24.53,261  +  205       25.    4,312  +  99  26.      8,432  +  761 

27.  31,845  +  301       28.  29,631  +  405       29.  293,476  +  310 
30.  82,437  +  3100  31.  23,976,124  +  51,000  32.  487,500  +  500 

33.  One  factor  of  5328  is  144.    Find  the  other.   (Problem.) 

34.  4™^  = 35.  13824^576     36>  132  x?=  121,836 


192  REVIEW  AND  PRACTICE  Written 

i.    How  many  pints  are  there  in  568  gallons  ? 

2.  A  grocer  buys  cinnamon  at  $.50  a  pound  and  sells  it 
at  5  cents  an  ounce,  a.  How  much  does  he  gain  on  a 
pound?     b.  On  53  pounds? 

3.  60,000  lb.  of  coal  at  $  5  per  ton  cost  how  much  ? 

4.  I  work  28  days  at  $2.50  a  day  and  take  14  tons 
of  coal  for  my  pay.  a.  How  much  is  my  labor  worth  ? 
b.  How  much  a  ton  do  I  pay  for  the  coal  ? 

5.  Subtract  the  sum  of  5  J  and  7 \  from  the  sum  of  8f 
and  9^-. 

6.  A  man  bought  3  sacks  of  flour  at  $  1.65  per  sack, 
and  4  bu.  of  corn  at  $  .75  per  bushel.  How  much  change 
should  he  receive  from  a  ten-dollar  bill? 

Quick  Test 

1.  How  many  gills  in  5  quarts  ? 

2.  In  how  many  hours  can  you  walk  12  miles  if  it  takes 
you  15  minutes  to  walk  one  mile  ? 

3.  What  is  the  cost  of  24  quarts  of  clover  seed  at  $  1  a 
peck? 

4.  Theodore  picked  15  quarts  of  berries  and  sold  |  of 
them  at  10  cents  a  quart.     How  much  did  he  receive  ? 

5.  What  is  the  smallest  number  that  exactly  contains 
either  3,  4,  or  6  ? 

6.  What  is  the  difference  between  -|  and  ^  ? 

7.  Two  and  one  half  quarts  of  milk  taken  from  a  can 
containing  2  gal.  leaves  how  many  quarts  ? 

s.   4800  ^  20  =  ?      9.   25  x  20  =  ?      10.    12  +  3£  =  ? 


Oral  and  Written        SURFACE  MEASURE  193 

1.  A  square  foot  is  how  many  inches  long  ?  Wide  ?  It 
contains  how  many  square  inches  ? 

2.  Draw  a  square  foot  on  the  blackboard,  cut  it  into 
square  inches.     How  many  are  there  ? 

3.  A  square  yard  is  how  many  feet  long  ?  Wide  ?  How 
many  square  feet  does  it  contain  ?  Show  it  by  a  drawing 
on  the  blackboard. 

4.  A  square  rod  is  how  many  yards  long?  Wide? 
What  would  you  do  to  find  how  many  square  yards  there 
are  in  1  square  rod  ?  5  J  x  5 J-  =  30 \.  How  many  square 
yards  in  one  square  rod  ? 

5.  About  how  many  square  rods  are  there  in  the  floor 
of  your  schoolroom  ? 

6.  A  piece  of  land  8  rods  wide  and  20  rods  long  con- 
tains an  acre  of  ground.  How  many  square  rods  does  it 
contain  ?  How  many  square  rods  make  an  acre  ?  Make  on 
the  blackboard  a  drawing  of  this  piece  of  land,  using  1  inch 
for  1  rod.  Make  it  into  lots  4  rd.  wide  and  8  rd.  long. 
These  are  good-sized  city  lots.     How  many  are  there  ? 

7.  If  your  school  ground  is  132  feet  from  front  to  rear 
and  165  feet  along  the  street,  it  contains  a  half  acre.  How 
many  square  feet  does  it  contain  ? 

8.  Draw  a  picture  of  a  field  28  rods  long  and  24  rods 
wide,  using  \  inch  for  a  rod.  How  many  square  rods  does 
it  contain  ? 

9.  Draw  a  picture  of  a  floor  35  feet  long,  containing 
1050  square  feet.  Use  \  inch  for  1  foot.  How  wide 
is  the  floor? 


194  SURFACE  MEASURE 

THE   TABLE   OF   SURFACE   MEASURE 

144  square  inches  (sq.  in.)  make  1  square  foot 

9  square  feet  (sq.  ft.)  make  1  square  yard 
30]  square  yards  (sq.  yd.)  make  1  square  rod 
160  square  rods  (sq.  rd.)  make  1  acre  (A.) 

Note.  —  In  working  the  following  examples,  first  answer  to  yourself 
these  questions  about  each  one :  a.  What  is  given  ?  b.  What  am  I  asked  tc 
Jindt    c.   Will  the  answer  be  greater  or  less  than  the  number  given? 

Oral 

1.  How  many  square  inches  in  12  sq.  ft.  ? 

2.  How  many  square  rods  in  \  A.  ? 

3.  A  floor  4  yd.  long  and  3  yd.  wide  contains  how 
many  square  yards  ?     How  many  square  feet  ? 

4.  The  front  of  a  desk  drawer  is  20  in.  long  and  5  in. 
wide.     It  contains  how  many  square  inches  ? 

Written 

1.  How  many  square  feet  in  437  sq.  yd.  ? 

2.  How  many  square  inches  in  94  sq.  ft.? 

3.  How  many  square  yards  in  48  sq.  rd.  ? 

4.  How  many  square  rods  in  26  A.  ? 

5.  How  many  square  yards  in  3933  sq.  ft.? 

6.  How  many  square  feet  in  13536  sq.  in.  ? 

7.  How  many  acres  in  4160  sq.  rd.  ? 

8.  Change  :  a.  124  A.  to  square  rods ;  b.  36  sq.  rd.  to 
square  yards ;  c.  523  sq.  yd.  to  square  feet ;  d.  12  sq.  ft. 
to  square  inches ;  e.  1  A.  to  square  rods,  to  square  yards, 
to  square  feet,  to  square  inches. 


Oral  SURFACE  MEASURE  195 

i.  The  area  of  a  rectangle  is  always  the  product  of 
what  two  factors  f 

2.  The  number  of  square  inches  in  a  rectangle  is  the 
product  of  ivhat  two  numbers  f 

3.  The  number  of  square  yards  in  a  rectangle  is  the 
product  of  what  two  numbers  ? 

4.  When  a  product  and  one  of  its  factors  are  given, 
how  can  you  find  the  other  factor  f 

5.  The  length  of  a  map  is  8  feet.  Its  width  is  5J  ft. 
What  is  its  area  ? 

6.  A  piece  of  pasteboard  20  inches  long  must  be  how 
wide  to  contain  120  square  inches  ? 

7.  A  rug  3  yd.  wide  and  4  yd.  long  covers  how  many 
square  yards  of  floor  ?     How  many  square  feet  ? 

8.  A  flag  is  3  yd.  long  and  2  yd.  wide.  It  is  how 
many  feet  long  ?  Wide  ?  Find  in  two  ways  the  number 
of  square  feet  in  it.     Make  pictures  to  prove  your  work. 

9.  A  door  mat  is  20  inches  by  30  inches.     Find  its  area. 

10.  Mrs.  Smith's  rose  bed  is  2  yd.  wide  and  covers  48 
sq.  yd.  of  ground.     How  long  is  it  ?     Find  its  perimeter. 

li.  Mr.  English  has  a  lawn  3  rd.  by  5  rd.  In  one  cor- 
ner is  a  summer  house  covering  1\  sq.  rd.  and  in  another 
corner  a  fern  bed  covering  \  sq.  rd.  How  much  surface 
is  left  for  grass  ?     (Picture,  using  1  in.  for  1  rd.) 

12.  Herbert  has  a  pansy  bed  4  ft.  by  12.  There  are 
2  plants  in  every  square  foot  of  ground.  How  many 
plants  in  the  bed? 


196  SURFACE  MEASURE  Written 

Change : 

l.  96000  sq.  rd.  to  acres.     2.    5616  sq.  in.  to  square  feet. 

3.  3429  sq.  in.  to  square  feet  and  square  inches. 

4.  1683  sq.  ft.  to  square  yards. 

5.  4346  sq.  ft.  to  square  yards  and  square  feet. 

6.  1837  sq.  rd.  to  acres  and  square  rodso 

7.  13  sq.  ft.  72  sq.  in.  to  square  inches. 

8.  43  sq.  yd.  7  sq.  ft.  to  square  feet. 

9.  48  sq.  rd.  13  sq.  yd.  to  square  yards. 
10.  12  sq.  yd.  4  sq.  ft.  to  square  inches. 

u.    14256  sq.  in.  to  square  feet ;  to  square  yards. 

12.  Find  the  area  of  a  door  mat  25  in.  by  36  in. 

13.  Mr.  Welton's  cornfield  is  25  rd.  by  32  rd.  a.  How 
many  square  rods  of  land  in  the  field  ?  b.  How  many 
acres  ?  c.  How  much  corn  does  it  yield  at  the  rate  of  46 
bu.  per  acre  ?  d.  How  much  is  the  corn  worth  at  $  .60 
per  bushel  ? 

14.  A  rectangular  farm  which  is  half  a  mile  long  must 
be  how  wide  to  contain  100  acres  ? 

Hint.  —  The  farm  must  contain  how  many  square  rods  ?  It  is  how  many 
rods  long? 

is.  How  many  square  inches  in  the  top  of  a  table  that 
is  4  ft.  long  and  3  ft.  wide  ? 

16.  At  45  cents  a  square  yard;  what  would  be  the  cost 
of  matting  to  cover  a  floor  15  ft.  by  18  ft.?  (This  may 
be  found  in  three  ways.) 

17.  6  A.  is  how  many  square  rods  more  than  4 J  A.  ? 


Written  SURFACE   MEASURE  197 

i.  Mr.  Hadley  owned  a  piece  of  land  39  rd.  by  24  rd. 
How  many  square  rods  had  lie  left  after  selling  %  of  an 
acre? 

2.  A  square  mile  is  how  many  rods  long  ?     Wide  ? 

a.  It  contains  how  many  square  rods  ? 

b.  It  contains  how  many  acres  ? 

3.  A  rectangular  church  floor  is  84  ft.  long  and  48  ft. 
wide.     It  covers  how  many  square  yards  of  land  ? 

4.  A  square  park  is  \  mi.  on  a  side.  a.  How  many 
square  rods  does  it  contain  ?  b.  How  many  square  yards  ? 
c.  How  many  acres  ?  d.  How  much  is  it  worth  at  $  200 
per  acre  ? 


132  ft, 


48  ft. 

S 

House. 

Grass. 

5.  a.  How  many  square  feet 
are  there  in  this  entire  lot  ? 
b.  How  many  square  feet  of 
ground  are  occupied  by  the 
house?  c.  How  many  square 
feet  of  grass  are  there  ? 

6.  A  man  cut  an  acre  of  land  into  5  building  lots  and 
sold  four  of  them.  The  first  contained  27f  sq.  rd.,  the 
second  36  sq.  rd.,  the  third  30^  sq.  rd.,  the  fourth  29f 
sq.  rd.  The  fifth  one  he  kept.  a.  How  many  square  rods 
of  land  did  the  man  sell  ?    b.  How  much  land  did  he  keep? 

7.  Mrs.  Rich  bought  a  rug  12  ft.  by  18  ft.,  and  another 
15  ft.  by  21  ft.  How  many  square  yards  of  floor  will 
both  rugs  cover  ? 

8.  What  is  the  cost  of  a  sidewalk  6  ft.  wide  in  front  of 
three  fifty-foot  lots  if  it  costs  14  cents  a  square  foot  ? 


198  REVIEW  AND  PRACTICE  Written 


Add: 

1.   397 

2.   $138.49 

3.   768 

4.   $12.99 

5. 

4086 

498 

6.52 

546 

6.28 

9798 

684 

8.79 

987 

143.72 

8469 

963 

7.56 

645 

24.08 

3578 

589 

109.84 

867 

16.49 

5946 

786 

3.58 

988 

4.45 

9894 

999 

17.75 

789 

9.78 

87.65 

6.    5£ 
4f 

3& 

7.    9f            8. 

5| 

13f 
15f 

H 

9.    13| 

H 

4& 

10. 

1»A 

16* 

12i 

Subtract : 

u.   14$ 

12.  7f 

13.     17f 

14.    18 

15. 

24 

H 

ii 

Jk 

14| 

ZiT8 

Multiply : 

is.   729 

17.  897 

is.  976 

19.  298 

20 

.   365 

38 

89 

76 

49 

Jl 

i^n<f  the  values : 

21     * 3  6  8 

22      19°8 

££.          18 

23.    Iff* 

24.    Iff* 

25. 

2625 
2  5 

26.  Add  the  difference  between  9835  and  4768  to  the 
difference  between  694  and  138. 

27.  Divide  the  product  of  96  and  55  by  the  product  of 
11  and  12. 


Oral  PRIME   AND  COMPOSITE  NUMBERS  199 

i.  What  is  a  factor  ?  Name  all  the  factors  of  4 ;  6 ; 
8;  10;  9;  18. 

2.  3  =  3x1.  3  and  1  are  what  of  3  ?  What  other 
factors  has  3  ? 

3.  7  =  7  x  1.  7  and  1  are  what  of  7  ?  What  other 
factors  has  7  ? 

4.  13  =  13  x  1.  13  and  1  are  what  of  13?  What 
other  factors  has  13  ? 

5.  What  factor  is  found  in  3,  7,  13?  How  does  the 
other  factor  of  each  of  these  numbers  compare  with  the 
number  itself?  Without  naming  the  factors,  tell  what 
are  the  factors  of  each  of  the  numbers,  3,  7,  and  13. 
Name  another  number  that  has  no  other  factor  than  itself 
and  one.     Name  several  such  numbers. 

6.  A  number  that  has  no  other  factors  than  itself  and 
one  is  a  prime  number. 

Name  all  the  prime  numbers  smaller  than  20. 

7.  What  is  true  of  4,  6,  8,  10,  9,  and  18  that  is  not 
true  of  2,  3,  5,  11,  and  17? 

8.  A  number  that  has  other  factors  than  itself  and  one  is 
a  composite  number. 

Name  all  the  composite  numbers  to  20. 
Tell  which  of  the  following  numbers  are  prime  and  ichich 
are  composite : 

9.  a.  8;  5;  9;  12;  24;  19;  33;  41;  17;  28;  37; 
29;  32;  15;  16;  18;  11;  23;  31;  40;  45. 

b.  The  number  of  hours  in  a  day ;  quarts  in  a  gallon ; 
cents  in  a  half  dime ;  cents  in  a  quarter ;  feet  in  a  yard 


200  PRIME   FACTORS 

1.  2  x  3  x  5  =  ?  2,  3,  and  5  are  what  of  30  ?  The\ 

are  what  kind  of  numbers  ? 

2.  7  x  5  =  ?  7  and  5  are  what  of  35  ?     They 

are  what  kind  of  numbers  ? 

3.  2  x  5  x  11  =  ?         2,  5,  and  11  are  what  of  110  ? 

They  are  what  kind  of  numbers  ? 

4.  What  two  things  have  you  found  true  of  each  of 
the  numbers  2,  3,  5,  7,  and  11  in  the  above  questions  ? 

5.  A  prime  number  used  as  a  factor  is  a  prime  factor. 
What  are  the  prime  factors  of  30?  Of  35?  Of  110? 
Of  10?     Of  14?    Of  12?     Of  8?    Of  21?     Of  25? 

6.  2  and  3  are  the  prime  factors  of  what  number? 
2  and  5?  5  and  3  ?  7  and  2  ?  2  and  11?  2,  3,  and  5  ? 
2,  3,  and  7  ?     2,  3,  and  11  ?     11,  2,  and  7  ? 

7.  Find  the  prime  factors  of  210 ;  of  540. 

We  divide  the  given  number 

by  the  smallest  prime  number 

that  will  divide  it,  using  the 

same  divisor  as  many  times  as 

possible.     We  then  divide  the 

quotient    by    the    next    larger 

prime  number  that  will  divide 

it,  and  so  on  till  the  quotient 

becomes  a  prime  number.     Each  quotient  becomes  the  dividend  for 

the  next  division.     The  last  quotient  and  all  the  divisors  are  the 

prime  factors  of  the  given  number. 

Find  the  prime  factors  of  the  following  numbers: 
8.   50      9.     45     io.     56     n.     72     12.    125     13.      75 
14.    96     15.    330     is.   420     17.    231     is.    385     19.    154 


2 
S 

5 

210 

105 

35 

7 

2 
2 
3 
3 

540 

270 

135 

45 

2.3.5.7  Arts. 

3 

15 

5 

2 

.2.3.3.3.5  Ana, 

Written  FACTORS  AND  MULTIPLES  201 

Find  the  prime  factors  of: 

1.     81         2.   400         3.   441         4.   294         s.   264 
6.   273         7.    595         s.   456         9.   184       10.   882 

11.  Of  what  number  are  2,  2,  3,  and   11  the  prime 
factors  ? 

12.  5,  7,  13,  and  19  are  the  prime  factors  of  what 
number  Sf 

13.  41  is  a  prime  factor  of  1763.     What  is  the  other  ? 

14.  Tell  which  of  the  following  numbers  are  prime  and 
which  are  composite:  50;  64;  71;  59;  52;  61;  63;  55. 

15.  Find  the  number  whose  prime  factors  are  11,  7, 
and  17. 

16.  The  product  of  three  prime  numbers  is  805.     Two 
of  the  numbers  are  7  and  5.     What  is  the  other  ? 

17.  The  product  of  three  numbers  is  2233.    The  product 
of  two  of  them  is  77.     What  is  the  third  ? 

is    §M  =  ?    385_x_3  =  ?     385  +  7     « 
'35  35x3      *      35+7 

442  +  2  =  9     442x3  =  9    442  +  17     » 
34  +  2      '      34x3      '      34  +  17 

20.  Dividing  both  dividend  and  divisor  by  the  same 
number  affects  the  quotient  how  ? 

21.  Multiplying  both  dividend  and  divisor  by  the  same 
uumber  affects  the  quotient  how  ? 

22.  2x3x5x7x11  =  ?     2x3x5x7  =  ?     2310  +  210=? 
2x3x5x7x11     a     3x11x17x19     a 


23. 


2x3x5x7  11x19 


202  CANCELLATION 

i.    Taking  a  factor  out  of  a  number  divides  the  number 
by  the  factor  taken  out,  thus: 
210  =  2x3x5x7 

2x3x5  =  30         ^=30 

2.  2730  =  2x3x7x13x5        65  =  5x13 

2730  =  2x3x7xX^  =  2x3x7  =  42     Quotient 
65  0xj£ 

3.  Taking  the  same  factor  from  both  dividend  and  divisor 
is  cancellation.  In  example  2  what  factors  were  taken  from 
both  dividend  and  divisor  ? 

4.  Find  the  quotients  by  cancellation : 

2x5x11x13  ,3x17x19x2 

o. 


d. 

f. 

7  x  6  x  21  J 

12x16x3x45x19  , 

g.  -  h. 

s: 


5x13 

4x 

:8x9x  11x14 

14  x  9  x  8 

21 

x7x3x5x6 

7  x  6  x  21 

12 

x  16x3x45x19 

19x3x12 

2310     2x£x5x7x 

n 

3: 

xl9 

8 

x8x 

12  x 

13x15 

15 

x8  x 

:13 

4 

x31 

x  50x6x9 

50 

x  6  x 

:4 

8 

xl7 

x  5  > 

:6x7 

5x8x7 

5x7  =  70     Quotient 

33  ?x/J 

Find  the  quotients  by  factoring  the  dividend  and  the 
divisor  and  canceling  : 

390  ,  '770     1925         ,  900  2736 

"•To"  &-"35"   C-~25"         d"W  ""W 

f   462    2310  ,  2x7x13x17   .  1932  .  2520 

7*  "14  9'     70        119      *'  23  x  2  3\     24 


CANCELLATION  203 

We  take  the  factor  2  out  of  12 

and  18;  the  factor  7  out  of  7  and  49; 
x    ffx?X^X^a210      the  factor  5  out  of  5  and  25.  and 

j  x  ;g  x  0  cancel  the  factor  9  from  both  divi 

dend  and  divisor.     The  factors  re- 
maining in  the  dividend  are  6,  7,  and  5.     6x7x5  =  210  Quotient 

7 

q*  We  take  the  factors  3  and  11  out  oi 

2»      o£  =  7  Quotient      both  dividend  and  divisor. 

» 

9£     9      79     11  70                                  ^e  *a^e  ^e  factor 

3.        ?x9xl2Q  ~W  =  7i  Quotient     12  out  of  72  and  120, 

^            **jL  then  the  factor  5  out 

™  of  25  and  10. 

36x27x49x50^9  7x4x24x2, 


4. 


70x18x15  2x7x12x2 

6.  (2x5x54)  +  (10x6)  =  2*5*54  =  ? 

10  x  6 

7.  (36  x  48  x  16) +  (27  x  24x8)  =  ? 

8.  Divide  25x2x72x14  by  6x9x120. 

9.  (Ilx3xl5xl4)  +  (21xllx3)  =  ? 

4x6xl0x20^9  8xl4x22xl8__9 

10*         12x25  '  ""2x11x7x3 

12.  What  is  the  quotient  of  4  x  9  x  17  x  80  divided  bj 
17x90? 

13.  (16x24x33x34)^(11x4x8x17)  =  ? 


204      PROBLEMS  SOLVED  BY  CANCELLATION 

i.    How  many  pineapples  at  8  cents  apiece  will  pay  for 
10  hours'  work  at  12  cents  an  hour  ? 

The  work  is  worth  (12  x  10)  cents. 
One  pineapple  is  worth  8  cents. 

(12  x  10)  cents  will  buy  -^— —  pineapples. 

o 


3      5 


=  15  pineapples  Answer. 


2.  A  farmer  exchanged  45  cabbages  at  9  cents  apiece 
for  sugar  at  5  cents  a  pound.  How  many  pounds  did  he 
receive  ? 

3.  A  milkman  sold  280  quarts  of  milk  at  6  cents  a 
quart  and  bought  corn  at  40  cents  a  bushel.  The  milk 
paid  for  how  many  bushels  of  corn  ? 

4.  William  traded  6  bushels  of  hickory  nuts  at  96  cents 
a  bushel  for  hens  at  48  cents  apiece.  How  many  hens 
did  he  get  ? 

5.  A  college  student  worked  72  days  in  vacation  at  $  3 
a  day.  If  all  his  expenses  in  college  amounted  to  $2  a 
day,  how  long  did  his  money  last  ? 

6.  How  many  bricks  8  inches  long  and  4  inches  wide 
are  required  to  cover  a  hearth  64  inches  long  and  32 
inches  wide  ?     (Picture.) 

7.  How  many  baskets  of  peaches,  each  containing  10 
quarts  worth  6  cents  a  quart,  must  be  given  for  18  bushels 
of  sweet  potatoes  at  60  cents  a  bushel  ? 


Oral  REVIEW  205 

i.    What  is  the  cost  of  30  tons  of  hay  at  $15  a  ton  ? 

2.  If  7  acres  of  land  cost  $200,  what  will  14  acres* 
cost? 

3.  3200  ounces  make  how  many  pounds  ? 

4.  When  1  lb.  of  tea  costs  20^,  what  must  be  paid  for 
J  of  a  pound  ?     For  J  of  a  pound  ? 

5.  A  owns  |  of  a  farm  and  B  f  of  it.  What  part  of 
the  farm  do  both  own  ?  If  C  owns  the  remainder,  what 
part  of  the  farm  does  C  own  ? 

6.  Will  has  $  2 \  and  James  $  3  J.  How  many  dollars 
have  both  ?     How  much  less  than  $10  ? 

7.  What  is  the  smallest  multiple  of  5,  2,  10,  and  4  ? 

Written 

i.  8  bu.  of  cranberries  were  put  in  quart  boxes  and  sold 
at  14  cents  a  box.  a.  How  many  boxes  were  there  ? 
b.  How  much  did  they  bring  ? 

2.  How  many  pints  in  5  bu.  of  birdseed  ? 

3.  How  many  ounce  weights  will  just  balance  8  lb.  ? 

4.  What  will  it  cost  at  18  9  a  square  yard  to  pave  a 
cellar  54  ft.  by  33  ft.  ? 

5.  How  many  hundredweight  in  5  sacks  of  feed,  each 
containing  120  lb.  ?     Solve  by  cancellation. 

6.  How  many  square  feet  in  246  sq.  yd.  of  paper? 

7.  Change  24  rods  to  yards  and  then  to  feet. 

8.  A  farmer  sold  J  of  his  flock  of  640  sheep,  a.  How 
many  did  he  sell  ?     b.  How  many  did  he  keep  ? 


206  REVIEW  Oral 

i.  £  is  how  many  24ths? 

2.  ^  is  how  many  18ths  ? 

3.  Add  \  and  \.     Subtract  |-  from  J. 

4.  Multiply  12  by  4J.     (Problem.) 

5.  A  rectangle  3  ft.  wide,  containing  24  sq  ft.,  is  how 
long  ?     What  is  its  perimeter  ? 

6.  How  many  square  inches  in  a  5-inch  square  ? 

7.  How  many  rods  of   fence  will  inclose  a  field  10^ 
rods  square  ? 

8.  A  cask  holds  48|  gal.  of  water.      If   20 J  gallons 
leak  away,  how  many  gallons  remain  ? 

Written 

1.  What  must  be  paid  for   12  tons  of   grate  coal  at 
$5.35  a  ton  and  4  tons  of  chestnut  coal  at  $5.50  a  ton? 

2.  If  10  men  earn  $  120  a  week,  what  will  6  men  earn 
at  the  same  rate  ? 

3.  Elsie  spent  J  of  $5  for  a  book  and  the  remainder 
for  a  pair  of  shoes.     What  did  the  shoes  cost  ? 

4.  At  $  .80  a  gallon,  what  is  the  cost  of  10  qt.  of  ice 
cream  ? 

5.  A  clock   that  ticks  twice   every  second  ticks  how 
many  times  in  an  hour  ? 

6.  If  a  bushel  of  corn  weighs  56  lb.,  how  many  bushels 
of  corn  in  a  car  load  weighing  14  tons  ? 

7.  1568  oz.  =  how  many  pounds  ? 


Oral  REVIEW  207 

1.  If  \  of  a  pound  of  coffee  costs  9  cents,  what  will 
2  lb.  cost? 

2.  240  bu„  of  oats  at  $.48  per  bushel  will  pay  for  16 
barrels  of  flour  at  what  price  per  barrel  ? 

3.  How  many  square  yards  in  4  sq.  rd.  ? 

4.  Read  DCCXXVIII. 

5.  How  many  square  feet  in  100  square  yards  ? 

6.  3  qt.  are  what  part  of  a  peck  ? 

7.  How  many  days  in  July  and  August  t 

Written 

1.  A  merchant  bought  44  yd.  of  silk  for  $  39.16  and 
sold  it  so  as  to  gain  $16.72.  a.  For  how  much  did  he 
sell  it  ?  b.  At  what  price  per  yard  did  he  sell  it  ?  c.  At 
what  price  per  yard  did  he  buy  it?  d.  What  did  he  gain 
on  a  yard  ? 

2.  How  many  half-bushel  baskets  will  hold  400  qt.  of 
cranberries  ? 

3.  Mr.  Rich  sold  his  horse  for  $275  and  his  carriage 
for  $125.  He  then  bought  an  automobile  for  5  times  as 
much  as  he  received  for  the  horse  and  carriage.  What 
did  the  automobile  cost  ? 

4.  A  farmer  shipped  to  the  city  32  cans  of  milk,  each 
can  containing  40  quarts,  a.  How  many  gallons  did  he 
ship  ?     b.  What  was  it  worth  at  2|  cents  a  quart  ? 

5.  How  many  yards  of  cloth  in  3  remnants  containing 
\  yd.,  2 1  yd.,  and  h\  yd.  respectively  ? 


208  REVIEW  Oral 

i.   Name  5  factors  of  30.  2.    5  x  ?  x  7  =  70. 

3.  At  6  cents  an  ounce,  what  must  be  paid  for  a  pound 
of  cloves  ? 

4.  Of  what  numbers  is  77  a  multiple  ? 

5.  At  10  cents  a  day,  what  is  the  cost  of  milk  for  a 
family  during  the  month  of  May  ?     April  ? 

6.  Read  3,050,120. 

7.  Name  the  letters  used  in  Roman  Notation  and  give 
the  value  of  each. 

Written 

1.  If  12  men  earn  $2880  in  a  certain  time,  how  much 
could  6  men  earn  in  the  same  time  ? 

2.  Add  nine  dollars  five  cents,  fourteen  dollars  sixteen 
cents,  forty-eight  cents,  two  dollars  five  cents,  and  seven- 
teen dollars  fifteen  cents. 

3.  a.  How  many  rods  in  \  of  a  mile  ?  6.  How  many 
feet? 

4.  Express  in  words  5,003,016. 

5.  The  divisor  is  234  and  the  quotient  108.  What  is 
the  dividend  ? 

6.  What  must  be  added  to  $63.75  to  make  $178.13? 

7.  Find  quotients  and  remainders  and  test  your  work : 


a. 


49  7  6  7,  42695        n      3  9  7  518        J     &3 0 \$  1 

18  6  °*       26  8         C-         13  7         °"         6l4 

P      425639  /  129675  n      683912  l     ""> 

t"    ~"2  5  3  /•    4  31  if*         9~T5  f(" 


19 
8.    Make  a  problem  for  6375  -i-  25. 


THE  MULTIPLICATION   TABLE 


209 


2x    1=    2 

3x    1=   3 

4x    1=   4 

5X1=5 

2x    2=   4 

3x    2=    6 

4x2=8 

ox    2  =  10 

2x    3=    6 

3x3=9 

4x    3  =  12 

5x    3  =  15 

2x    4=    8 

3  x    4  =  12 

4  x    4  =  16 

5x    4  =  20 

2x    5  =  10 

3  x    5  =  15 

4x    5  =  20 

5x    5  =  25 

2x    6  =  12 

3x    6  =  18 

4  x    6  =  24 

5x    6  =  30 

2x    7  =  14 

3  x    7  =  21 

4x    7  =  28 

5x    7  =  35 

2x    8  =  16 

3x    8  =  24 

4  x    8  =  32 

5x    8  =  40 

2x    9  =  18 

3  x    9  =  27 

4x    9=36 

5x    9  =  45 

2  x  10  =  20 

3  x  10  =  30 

4  x  10  =  40 

5  x  10  =  50 

2  x  11  =  22 

3  x  11  =  33 

4  x  11  =  44 

5  x  11  =  55 

2  x  12  =  24 

3  x  12  =  36 

4  X  12  =  48 

5  x  12  =  60 

6x    1=   6 

7x    1=    7 

8x    1=   8 

9x    1=     9 

6x    2  =  12 

7x    2  =  14 

8x    2  =  16 

9x    2=   18 

6x    3  =  18 

7  x    3  =  21 

8x    3  =  24 

9x    3=   27 

6x    4  =  24 

7  x    4  =  28 

8x    4  =  32 

9  x    4  =   36 

6x    5  =  30 

7x    5  =  35 

8  x    5  =  40 

9x    5=   45 

6  x    6  =  36 

7  x    6  =  42 

8x    6  =  48 

9x    6=   54 

6x    7  =  42 

7  x    7  =  49 

8x    7  =  56 

9x    7=    63 

6  x    8  =  48 

7x    8  =  56 

8x    8  =  64 

9x    8=    72 

6  x    9  =  54  * 

7  x    9  =  63 

8x    9  =  72 

9x    9=   81 

6  x  10  =  60 

7  x  10  =  70 

8  x  10  =  80 

9x10=    90 

6  x  11  =  66 

7  X  11  =  77 

8x11  =  88 

9x11=   99 

6x12  =  72 

7  x  12  =  84 

8  x  12  =  96 

9  x  12  =  108 

10  x    1=   10 

11  X    1=    11 

12  x    1=   12 

Roman 

10  x    2=   20 

11  X    2  =   22 

12  x    2=   24 

Numerals 

10  x    3=   30 

11  x    3  =   33 

12  x    3=   36 

10  x    4=   40 

11  x    4  =   44 

12  x    4=   48 

I  =1 

10  x    5  =   50 

11  X    5  =   55 

12  x    5=    60 

V=5 

10  x    6  =    60 

11  X    6  =    66 

12  x    6  =   72 

X  =  10 

10  x    7=    70 

11  x    7  =   77 

12  x    7=   84 

L  =50 

10  x    8=   80 

11  X    8  =   88 

12  x    8  =   96 

C  =100 

10  x    9=    90 

11  x    9  =   99 

12  x    9  =  108 

D=500 

10  x  10  =  100 

11  X  10  =  110 

12  x  10  =  120 

10  x  11  =  110 

11  x  11  =  121 

12  x  11  =  132 

M  =  1000 

10  x  12  =  120 

11  x  12  =  132 

12  x  12  =  144 

M  =  1,000,000 

210 


TABLES 


LIQUID  MEASURE 

4  gills  (gi. )  =  1  pint  (pt. ) 
2  pints  =  1  quart  (qt.) 
4  quarts  =  1  gallon  (gal.) 


DRY  MEASURE 

2  pints  (pt.)  =  1  quart  (qt.) 
8  quarts  =  1  peck  (pk.) 
4  pecks  =  1  bushel  (bu.) 


UNITED   STATES   MONEY 

10  mills  =  1  cent 
10  cents  =  1  dime 
10  dimes  =  1  dollar 
10  dollars  =  1  eagle 


AVOIRDUPOIS   WEIGHT 

16  ounces  (oz.)  =  1  pound  (lb.) 
2000  pounds  =  1  ton  (T.) 
100  pounds  =  1  hundredweight 
(cwt.) 


LINEAR   MEASURE 

12  inches  (in.)  =  1  foot  (ft.) 
3  feet  =  1  yard  (yd.) 

5}jrfdM=i^(rd.) 

or  16 1  feet  J  ' 

320  rods  =  1  mile  (mi.) 


TIME 

60  seconds  (sec)  —  1  minute 

(min.) 
60  minutes  =  1  hour  (hr.) 
24  hours  =  1  day  (da.) 

7  days  =  1  week  (wk.) 

365  days  =  1  common  year 

366  days  =  1  leap  year 


SQUARE  MEASURE 

144  square  inches  (sq.  in.)  =  1  square  foot  (sq.  ft.) 
9  square  feet  =  1  square  yard  (sq.  yd 


square  feet 
30 |  square  yards 
160  square  rods 


1  square  yard  (sq.  yd.) 
=  1  square  rod  (sq.  rd.) 
=  1  acre  (A.) 


Addition,  33-40,  43,  44. 

Of  dollars  and  cents,  41. 
Addition  and  subtraction,  47,  53,  86. 

Of  fractions,  157,  159,  161,  163,  165, 
167,  169,  171,  173. 
Area,  131. 
Avoirdupois  weight,  103,  187. 

Bushel,  72. 

Cancellation,  202,  203. 
Counting,  1,  2. 

Days  in  different  months,  92. 

Days  of  the  week,  7. 

Division,  65,  75,  76,  105,  115,  129,  132, 

186,  191. 
Drill  tables, 

Addition,  31. 

Multiplication,  73,  77. 

Subtraction,  31. 
Dry  measure,  181. 

Factors,  142,  144. 
Factors  and  multiples,  201. 
Finding  any  part  of  a  number,  93. 
Foot,  15,  122. 
Fractions, 

Addition  and  subtraction  of,  126, 
150-154,  157,  159,  161,  163,  165, 
167,  169,  171,  173. 

Halves,  fourths,  and  eighths,  122, 
146. 

Lowest  terms,  148. 

One  half,  9. 

One  third,  17. 

One  fourth,  20. 

Terms  of,  147. 


INDEX 

Gallon,  18. 
Inch,  22. 


Linear  measure,  188,  189. 
Liquid  measure,  179. 

Making  change,  116. 

Making  questions,  110. 

Miscellaneous  problems,  92,  94,  98,  99, 

117,  118,  120,  121,  123. 
Money,  41. 
Multiples,  145. 
Multiplication,  61,  62,  69,  72,  89,  90, 

102,  119. 
Multiplication  and  division,  59,  60,  68, 

70,  71,  77,  78,  80,  100,  106,  109; 

114,  126,  128,  130. 

Odd  and  even  numbers,  141. 

Peck,  72. 

Perimeter,  127. 

Pint,  5. 

Prime  and  composite  numbers,  199. 

Prime  factors,  200. 

Problems, 

In  addition,  43. 

In  fractions,  156. 

In  temperature,  54. 

In  time,  185. 

Of  two  steps,  160. 

Solved  by  cancellation,  204. 

Quart,  5,  72. 

Quick  tests,  91,  95, 107,  143. 


Reading  numbers,  3,  32,  84,  124 


211 


212 


INDEX 


Rectangles,  112,  113. 
Review,  56-58,  63,  66,  67,  73,  79,  81, 
82,  88,  91,  97,  101,  104,  108,  111, 
125,  133-138,  155,  158,  162,  164, 
166,  168,  170,  172,  174,  178,  180, 
182,  190,  192,  198,  205,  208. 
Roman  numerals, 
To  five,  8. 
To  twelve,  11. 
To  twenty,  20. 
To  twenty-four,  28. 
To  one  hundred,  64. 
To  one  thousand,  1 16. 

Subtraction,  45,  46,  48-62,  87. 


Surface  measure,  193-197. 

Tables, 

Of  addition,  31,  66. 

Of  denominate  numbers,  210. 

Of  multiplication,  73,  74,  77,  ! 

United  States  money,  175-177. 

Whole  and  mixed  numbers,  149. 
Writing  numbers,  3,  32,  84,  124. 
Of  dollars  and  cents,  41. 

Yard,  16. 


M305881 


THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


GENERAL  LIBRARY 
UNIVERSITY  OF  CALIFORNIA— BERKELEY 

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